Turn out the brownie onto a work surface and peel away the parchment paper. Place a 2-quart bombe mold or metal mixing bowl on top of the brownie and using a knife, cut out the shape of the mold. Crumble the trimmings into a bowl to use as garnish on the final bombe. Wrap and set aside the large brownie for final assembly.
Lightly coat the bombe mold or metal mixing bowl with vegetable oil. Chill in the freezer for 30 minutes to 1 hour. Meanwhile, soften the Coffee Ice Cream in the refrigerator (but do not let melt).
Remove the mold from the freezer. Using a rubber spatula, quickly spread an even, thick layer of the softened Coffee Ice Cream over the mold to within about 1 1/2 inches of the top. Cover with plastic wrap, pressing to seal the ice cream against the mold and remove any air pockets. Return to the freezer to harden. Meanwhile, soften the Hazelnut Ice Cream in the refrigerator (but do not allow to melt).
Remove the mold from the freezer. With a spatula, fill the center of the mold with the softened Hazelnut Ice Cream, leaving a 1 1/2-inch space along the top to place the brownie cake. Wrap in plastic wrap and return to the freezer to harden slightly.
Remove the mold from the freezer and while the Hazelnut Ice Cream is still slightly soft, press the brownie onto the ice cream to form a base. Wrap in plastic and return to the freezer to harden completely, at least 4 hours.
To make the sweetened whipped cream, in a bowl, beat 1 1/2 cups of the cream with an electric mixer at medium speed until it thickens and starts to hold soft peaks. Add the sugar and vanilla and continue beating until the cream holds peaks, being careful not to overbeat. Refrigerate while assembling the other ingredients.
To make the Hazelnut Chocolate Sauce, in a medium saucepan, bring the remaining 1 cup of cream and Frangelico to a gentle boil. Remove from the heat. Place the chocolate in a medium bowl and pour the warm cream mixture over it. Let sit for 2 minutes, then whisk until melted and well blended. Whisk in the hazelnuts.
Remove the bombe from the freezer. To unmold, dip in a pan or sink of warm water. Invert onto a platter or cake plate and carefully remove the mold. (If the ice cream has softened a great deal, return to the freezer to harden.)
To serve the bombe, spread an even layer of sweetened whipped cream over the bombe and drizzle with the chocolate sauce. Crumble the reserved brownie crumbs over the top and present tableside.
To serve, cut with a sharp knife that has been dipped in hot water and wiped with a clean cloth before slicing each piece. Serve immediately.
Preheat the oven to 350 degrees F.
Grease a 9-inch round baking pan. Line with parchment paper and lightly grease and flour the paper and sides of the pan, shaking to remove any excess. Set aside.
In a saucepan over low heat, melt together the butter and chocolate, stirring occasionally. Add the sugar and stir to dissolve and until smooth. Remove from the heat and pour into a medium bowl. Add the flour and eggs in 2 additions, alternating, and whisking well after each to combine. Add the vanilla and mix well. Pour into the prepared pan and rap the bottom of the pan lightly against the countertop. Bake until the brownies are set and have risen, and a cake tester inserted into the middle comes out clean, 25 to 30 minutes.
Remove from the oven and let cool.
Preheat the oven to 350 degrees F.
Spread the hazelnuts on a baking sheet. Bake for about 10 minutes, stirring occasionally until the skins are cracked and the nuts (under the skins) are deeply golden brown. Place the nuts in a towel and rub them to remove most of the skins. Cool completely.
Combine the cream and 1 cup of the milk in a large heavy saucepan. Scrape the vanilla seeds into the cream mixture and add the bean and the hazelnuts. Bring to a gentle boil over medium heat.
Whisk the yolks and sugar in a medium bowl. In a slow, steady stream, whisk 1 cup of the hot cream mixture into the egg mixture. Gradually whisk the egg mixture back into the saucepan. Stir constantly over medium-low heat until the mixture thickens enough to coat the back of a spoon and reaches 170 degrees F on an instant-read thermometer, about 5 minutes. Strain through a fine-mesh sieve into a heatproof medium bowl.
Discard the vanilla bean, remove the nuts and rinse in a strainer under cold running water; pat dry on paper towels. On a work surface, crush the nuts with a meat mallet or rolling pin, and stir into the custard. Stir in the remaining 1 cup milk and the liqueur. Cover with plastic wrap, pressing the wrap against the surface of the custard to prevent a skin from forming. Refrigerate until well chilled, at least 2 hours.
Pour the chilled custard into the bowl of an ice cream machine and process according to the manufacturer's instructions. Place in a plastic container, cover tightly, and freeze until ready to use.
In a medium saucepan, combine the milk, cream, 1/2 cup of the sugar, and coffee. Bring to a gentle boil, stirring occasionally to dissolve the sugar. Remove from the heat.
In a medium bowl, beat the yolks with the remaining 1/2 cup of sugar until the yolks are thick and light yellow in color, about 3 minutes.
Temper the eggs by adding about 1 cup of the warm milk mixture to the eggs, whisking to combine. Gradually add the egg mixture in a slow, steady stream, to the remaining hot milk. Cook over medium-low heat, stirring occasionally, until the mixture thickens enough to coat the back of a spoon, about 5 minutes. Remove from the heat and strain through a fine mesh strainer into a clean container. Cover with plastic wrap, pressing down against the surface to keep a skin from forming. Refrigerate until well chilled, at least 3 hours.
Pour the custard into the bowl of an ice cream machine and process according to the manufacturer's instructions. Place in a plastic container, tightly cover, and freeze until ready to use.