Place the flour, sugar, and salt in the bowl of a food processor and pulse two or three times to combine. Add the butter and continue pulsing until the mixture resembles coarse meal. Add the water by drizzling about 1 tablespoon at a time, pulsing after each drizzle. Stop once the dough begins to come together.
Transfer the dough to a board and use the heel of your hand or a pastry scraper to press it together. Pat into a disk approximately 6 inches in diameter, wrap in plastic wrap, and refrigerate until firm, about 2 hours.
On a lightly floured board, roll out the dough to a 13 to 14-inch circle, flouring the dough and board as necessary to keep it from sticking. Roll up the dough around the rolling pin and unroll it into the tart pan. Gently lift the edges to ease the dough into the corners of the pan, then push the dough down gently to be certain the dough around the sides is 1/4 inch thick. Use a paring knife to cut excess dough from the rim of the pan. If necessary, pat a bit of the dough trimmings into any thin spots. Cover with plastic wrap and refrigerate for 1 hour.
Position a rack in the middle of the oven and preheat the oven to 375degreesF. Place the tart pan on a baking sheet.
Prick the bottom of the crust with a fork, line with aluminum foil or parchment paper, and fill with pie weights or dry beans. Bake for 15 minutes.
Remove the parchment and weights, and continue to bake for 15 to 20 minutes, or until the crust is golden. Sprinkle the chopped chocolate evenly over the bottom of the crust and bake for an additional minute, just to melt the chocolate. Remove from the oven and use the back of a spoon or a small offset spatula to spread the chocolate in an even layer. Let cool on a rack while you prepare the filling. Raise the oven temperature to 400degreesF.
To make the filling:
In a medium saucepan, combine the sugar and water and stir over medium-low heat until the sugar dissolves. Increase the heat to medium-high and cook, without stirring, swirling the pan so the caramel colors evenly. If sugar crystals form on the sides of the pan, brush with a wet pastry brush. Test the color of the caramel by drizzling a few drops onto a white plate. When the color is medium to dark amber, remove from the heat. Slowly and carefully - it will bubble up - add the cream.
Return the caramel to medium heat and cook for 3 minutes to thicken slightly, reducing the heat to medium-low if the caramel bubbles too much. Remove from the heat and cool for 15 minutes.
Place the tart shell on a baking sheet.
In a medium bowl, whisk together the vanilla, egg, and yolk. Slowly whisk into the caramel. Stir in the melted butter, followed by the nuts and nibs, if using. Pour the filling into the prepared tart shell. The filling will come to the top of the shell. (If the crust has shrunk during baking, it may not hold all the filling.)
Bake the tart for 15 minutes. Lower the oven temperature to 375degreesF and bake for an additional 15 minutes, or until the filling is set.
Let cool on a rack for about 10 minutes. While still warm, move the tart in the pan to loosen the edges where the caramel has stuck, but keep it in the pan.
Let cool completely before removing the tart ring.
Serve each wedge of tart with a dollop of the cocoa whipped cream.
Cocoa Whipped Cream:
Place the cream in a chilled metal bowl or mixer bowl. With a whisk, or the whisk attachment, whip the cream until slightly frothy. Combine the sugar with the cocoa powder. Sprinkle into the cream and continue to whip until soft peaks form. Use immediately, or refrigerate for up to 1 hour.