For the Chocolate Pate Sucre tart crust:

Place the flour, cocoa, sugar, salt and butter in a stand mixer and beat on low speed until it resembles coarse crumbs or has the appearance of wet sand. In a separate bowl, combine the egg, heavy cream and vanilla extract and whisk until blended. Add the wet mixture to the dry mixture and mix just until combined, about 20 seconds. Remove the dough from the cake mixer and spread on a clean work surface. Knead until well incorporated and wrap with plastic wrap and chill for about 1 hour.

Preheat the oven to 375 degrees F.

Remove the dough from the refrigerator and bring to room temperature, about 15 minutes. Sprinkle a clean work surface with flour and roll the dough out to a 14-inch circle. Lay the dough into an 11-inch tart shell with a removable bottom. The dough is fragile and will crumble; don't be alarmed. Just pinch the separated pieces back together and press into the bottom and sides of the tart pan.

Line the tart shell with parchment paper and add pie weights. Blind-bake the dough for 10 minutes, remove the pie weights and parchment paper from the pan and return the pan to the oven to bake an additional 5 minutes. Remove and allow to cool completely before adding the filling mixture.

For the Souffle Tart filling:

Set a medium stainless steel bowl over a 2-quart pan with 2 cups of water in it. Set the heat to medium-low and add the butter and chocolate to the pan. Cook, stirring occasionally, until the chocolate and butter are thoroughly melted. Remove from the heat. In a standing mixer combine the eggs and sugar and beat, using a whip attachment on medium speed, until pale yellow and thick, about 1 minute. Fold the melted chocolate and flour into the egg mixture and pour into the prepared tart shell. Place in the oven and bake until the batter is set, 18 to 20 minutes. Allow to completely cool before serving.

Heat the heavy cream, coconut milk and whole milk in a heavy-bottomed saucepan over medium heat. Place the eggs and sugar in a heatproof mixing bowl and beat until pale yellow in color and all of the sugar has dissolved. Temper about 1/2 a cup of the cream mixture into the egg mixture and whisk vigorously to incorporate well. Add the egg mixture to the saucepan with the cream mixture, lower the heat slightly, and cook, stirring constantly with a whisk or wooden spoon, until the custard has thickened enough to coat the back of a spoon, 4 to 5 minutes.

Remove from the stove and strain the custard through a fine mesh sieve into a clean bowl. Place the bowl in another bowl half-filled with ice and water. Stir occasionally until chilled.

Pour the chilled custard into an ice cream machine and process according to the manufacturer's instructions until frozen. Transfer to an airtight container and freeze until ready to serve.

Yield: about 1 quart