Chess Pie with Blackened Pineapple Salsa and Caramel Sauce

Ingredients:
1 1/2 cups all-purpose flour
3 tablespoons granulated sugar
3/4 teaspoon salt
3 1/2 tablespoons cold unsalted butter, cut into small pieces
2 tablespoons cold vegetable shortening (trans-fat-free)
4 to 5 tablespoons ice water
3 tablespoons peanut or vegetable oil, divided
1 pineapple (preferably labeled "extra sweet"), peeled and sliced crosswise into 1/2-inch-thick rounds
1 tablespoon grated lime zest
1/4 cup fresh lime juice
1 tablespoon dark rum
3 tablespoons packed light brown sugar
1 cup granulated sugar
1/4 cup water
2 tablespoons unsalted butter, softened
1/2 cup heavy cream at room temperature
1 1/2 tablespoons plain Greek-style yogurt at room temperature
4 whole large eggs
2 large egg yolks
1 1/2 cups granulated sugar
3 tablespoons unsalted butter, melted
2 1/2 tablespoons cornmeal
1/2 cup well-shaken buttermilk
1 /2 teaspoon kosher salt
1 1/2 teaspoons pure vanilla extract
1/2 teaspoon grated nutmeg
Equipment: a 9-inch round tart pan (1 inch deep) with removable bottom; pie weights or dried beans

Instructions:
Stir together flour, sugar, and salt in a large bowl (or pulse in a food processor). Add butter and shortening and blend with your fingertips or a pastry blender (or pulse) just until mixture resembles coarse meal with some roughly pea-size butter lumps. Drizzle 4 tablespoons ice water evenly over mixture and gently stir with a fork (or pulse) until incorporated.
Squeeze a small handful: If dough doesn't hold together, add more ice water, 1/2 tablespoon at a time, stirring (or pulsing) until incorporated. (Do not overwork dough or pastry will be tough.)
Turn out dough onto a work surface and form into a ball, then flatten into a 5-inch disk. Chill, wrapped in plastic wrap, until firm, at least 1 1/2 hours.
Heat 2 tablespoons oil in a 12-inch heavy skillet over high heat until it shimmers. Sear pineapple in 2 batches, turning once, until well blackened, about 6 minutes per batch, adding remaining tablespoon oil between batches. Transfer to paper towels to drain and cool briefly, then cut pineapple into 1/4-inch pieces, discarding core.
Whisk together lime zest, lime juice, rum, and brown sugar in a medium bowl. Stir in pineapple and chill until ready to use.
Bring sugar and water to a boil in a 10-inch heavy skillet, stirring until sugar has dissolved, then wash down any sugar crystals from side of skillet with a pastry brush dipped in cold water. Boil, without stirring, swirling pan occasionally, until dark amber, 7 to 8 minutes. Cool 2 minutes, then whisk in butter, cream, and yogurt. Transfer to a bowl and chill.
Preheat oven to 375°F with rack in middle.
Roll out dough on a lightly floured surface with a lightly floured rolling pin into an 11-inch round (about 1/8 inch thick), then fit into tart pan. Trim excess dough flush with rim, then press side to make dough come up slightly above rim. Lightly prick bottom all over with a fork, then chill 30 minutes.
Line tart shell with foil and fill with pie weights. Bake on a baking sheet until side is set and edge is pale golden, about 15 minutes. Carefully remove foil and weights and continue to bake until pale golden all over, about 25 minutes more, loosely covering edges with foil if they get too dark. Cool shell in tart pan 15 minutes.
Reduce oven temperature to 350°F.
Whisk together eggs, yolks, and sugar in a large bowl, then whisk in remaining ingredients. Transfer filling to tart shell and bake until a light crust forms on top and filling is set 3 inches from edge but center is still wobbly, 45 to 50 minutes (filling will be slightly puffed and will continue to set as it cools).
Serve slightly warm or at room temperature, topped with pineapple salsa and drizzled with caramel sauce.