Put the sliced butter in a small bowl and place it in the freezer. Fill a medium liquid measuring cup with water and add plenty of ice. Let both the butter and the ice eater sit and get very cold for 5 to 10 minutes.

In the bowl of a stand mixer fitted with a paddle, mix the flour, sugar, and salt on low speed until combined. Add half of the chilled butter and mix on low speed until the butter is just starting to break down, about 1 minute. Add the rest of the butter and continue mixing until the butter is broken down in various sizes (some butter will be incorporated into the dough, some will be a bit large, but most should be about the size of small peas.) Stop the mixer and use your hands to check for any dry patches of dough on the bottom of the bowl; incorporate the dry flour as best you can. With the mixer running on low speed, slowly add about 1/4 cup [60 g] of the ice water and mix until the dough starts to come together but is still quite shaggy (if the dough is not coming together, add more water, 1 tablespoon at a time, until it does.)

Dump the dough out onto a lightly floured work surface and flatten it slightly into a square. Gather any loose/dry pieces that won’t stick to the dough and place them on top of the square. Gently fold the dough over onto itself and flatten again. Repeat this process three or four more times, until all the loose pieces are worked into the dough, being careful not to overwork the dough. Flatten the dough one last time into a 6 in [15 cm] disk. Refrigerate for 30 minutes before using.

When ready to use, lightly flour a work surface and roll the dough to a 12 in [30.5 cm] circle. Gently fold the dough in quarters and place it into a 9 in [23 cm] pie plate. Unfold the dough, letting the excess dough drape over the edges. Gently press the dough into the bottom and trim the overhang to 1 in [2.5 cm] past the lip. Tuck the overhang, so the folded edge lies on the edge of the pan. Crimp the edge of the dough, using your fingers. Place the pie plate in the freezer until firm, 20 to 30 minutes.

Adjust and oven rack to the lowest position. Preheat the oven to 400F [200C]. Place a baking sheet on the oven rack (the preheated baking sheet helps crisp the bottom of the pie crust). Remove the pie plate from the freezer and line the pie shell with parchment paper, covering the edges to prevent burning. Fill the center with pie weights.

Bake the pie shell 25 to 28 minutes, until the dough is light golden brown and no longer wet. Remove the pie plate from the oven and carefully remove the pie weights and parchment paper. Return the pie plate to the oven and continue to bake 8 to 12 minutes, until golden brown. Transfer the pie plate to a wire rack and let cool completely.

Place the chocolate in a small bowl. Heat the heavy cream in a small saucepan until it is simmering and just about to boil. Pour the cream over the chocolate, cover the bowl with plastic wrap, and let sit for 5 minutes.

Remove the plastic and whisk until completely smooth. Pour the ganache over the cooled pie shell, and smooth with an offset spatula. Move the pie to the fridge and let the ganache set.

Heat 1 cup [240 g] of the heavy cream in a small, heavy saucepan until just hot.

In a medium saucepan off the heat, whisk the egg yolks. Whisking constantly, slowly add the sugar to the egg yolks, then the salt, and then slowly pour in the warmed heavy cream. Cook over medium heat, stirring constantly, until the mixture thickens and coats the back of a spoon – this usually happens at 160F [70C] (the custard will thicken as it cools). Pour the mixture through a fine-mesh sieve into a large bowl and stir in the vanilla.

In a small saucepan over low heat, melt the chocolate, stirring frequently until smooth. Whisk the chocolate into the custard until smooth, then let cool.

In the bowl of a stand mixer fitted with a whisk, beat the remaining 1 1/2 cups [360 g] of heavy cream until stiff peaks form. Whisk one-third of the whipped cream into the chocolate custard to lighten in, then gently fold in the remaining whipped cream. Transfer the mousse to the pie shell and place it over the chilled ganache. Use an offset spatula to spread it in an even layer. Chill the pie for at least 4 hours and up to overnight (I cover the top of the pie with a loose piece of parchment paper. Wrapping it in plastic can make the crust less flaky).

In the bowl of a stand mixer fitted with a whisk, beat together the mascarpone cheese, sugar, and salt on low speed until combined. Increase the speed to medium and beat until light, 2 to 3 minutes. On low speed, slowly add half the cream until combined, then stop the mixer and scrape down the sides of the bowl, making sure the cheese is completely combined into the cream. Add the rest of the cream on low speed. Increase the speed to medium-high and beat until the cream is smooth, thick, and nearly double in volume. When the pie is set, top with the whipped cream.