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To make the crust: In a medium bowl, whisk together the flours and salt.
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Add the shortening, working it in until the mixture is evenly crumbly, like coarse beach sand; you want everything thoroughly combined.
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Add the butter to the flour mixture, and begin to work it in with your fingertips, a pastry cutter, or a mixer. Don't be too thorough; the mixture should be uneven with big chunks of butter in among the smaller ones.
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Add 2 tablespoons of the water and toss to combine.
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Slowly add additional water, a tablespoon at a time, until you have a chunky mixture that barely holds together when squeezed. The mixture may look quite dry.
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Shape the dough into a disk about 1" thick and refrigerate it for 30 minutes or longer; this rest allows the flour to absorb the water, making the dough easier to roll out. If you decide to let the dough chill longer than 30 minutes, allow it to rest at room temperature for 10 to 15 minutes before rolling to allow the butter to soften up a bit.
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Roll the dough into a 13" circle about 1/8” thick. Transfer the dough to a 9" pie pan, trim and crimp the edges, and place the pan in the refrigerator for 30 minutes.
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To parbake the crust: Preheat the oven to 400°F. Position one rack in the lower third and one rack in the middle of the oven.
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Remove the chilled crust from the refrigerator, line it with foil or parchment, and fill it with pie weights (or dried beans, uncooked rice, or granulated sugar).
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Place the pie pan on a baking sheet and bake the crust on the lower oven rack for 15 to 20 minutes, until the top edges begin to turn light brown. Remove from the oven and carefully lift the parchment and weights out of the pan. Reduce the oven temperature to 375°F.
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To make the chocolate bottom: While the pie is parbaking, combine the chocolate and cream in a small, microwave-safe bowl. Heat the mixture in 20-second increments at 50% power, stirring between each interval, until smooth. Alternatively, combine the chocolate and cream in a small saucepan and cook over medium-low heat, stirring frequently, until smooth.
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Spread the chocolate mixture evenly across the bottom of the parbaked pie crust. (A small offset spatula is a helpful tool here.) Place the pie in the refrigerator and chill until the chocolate has fully set, about 45 to 60 minutes.
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To make the chess pie filling: In a large bowl, combine the sugar, cornmeal, flour, and salt. Add the cream, vinegar, eggs, and extracts and whisk until smooth. Add the melted butter and continue whisking until smooth.
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Once the chocolate bottom is firm, pour the prepared filling into the pie crust and place the pie pan on a baking sheet. Sprinkle the sliced almonds and sparkling sugar over the top of the pie, then transfer to the middle rack of the oven.
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Bake the chess pie for 35 minutes, then cover the edges of the crust with a pie shield or strips of aluminum foil. Bake for an additional 15 to 20 minutes, until the center is just barely set and the top is golden brown. When a digital thermometer is inserted 1" from the edge of the crust, it should read 195°F.
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Remove the chess pie from the oven and let it cool completely before cutting: about 2 to 4 hours at room temperature or about 1 hour if chilled in the refrigerator.
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Storage information: Store any leftover almond chess pie in the refrigerator, covered, for several days.
