Prepare the crust: Pulse pecans in a food processor until finely chopped. Add next 4 ingredients; pulse until well combined, 3 or 4 times. Add butter and shortening; pulse until mixture looks like coarse meal, 5 or 6 times. Drizzle buttermilk over mixture; pulse just until dough begins to come together. Shape into a flat disk. Wrap in plastic wrap; chill 2 hours or up to 2 days.

When ready to use, let dough sit at room temperature until soft to the touch, 20 to 30 minutes. Unwrap dough; roll out on a lightly floured surface into a 12- to 13-inch circle. Fit into a 9-inch pie plate. Fold edges under; crimp. Prick bottom of dough a few times with a fork; freeze 15 minutes.

Preheat oven to 375°F. Line dough with parchment paper; fill with pie weights or dried beans. Bake until edges are lightly golden and just set, about 15 minutes. Remove parchment and weights; continue baking until bottom of crust is set, 8 to 10 more minutes. Transfer to a wire rack; cool completely, about 30 minutes.

Prepare the Pecan Pie Filling: Reduce oven temperature to 350°F. Chop 2 cups of the pecan halves; reserve remaining 1 1/2 cups pecan halves. Spread chopped pecans in a single layer on a baking sheet. Bake until lightly toasted, about 5 to 6 minutes. Cool completely, about 30 minutes.

Whisk eggs until smooth and well combined. Add corn syrup, brown sugar, vanilla, cornmeal, and salt; whisk until thickened and smooth. Set aside 3 tablespoons of mixture.

Prepare the Dulce de Leche-Cheesecake Filling: Beat cream cheese, egg, vanilla, and salt in a medium bowl with an electric mixer fitted with paddle attachment on medium speed until very creamy and smooth, 1 minute. Add dulce de leche; beat until well combined, 1 minute. Spoon into prepared crust. Sprinkle toasted chopped pecans over cream cheese mixture in crust. Gently spoon Pecan Pie Filling over chopped pecans.

Reduce oven temperature to 325°F. Toss reserved 1 1/2 cups pecan halves with 3 tablespoons reserved Pecan Pie Filling. Arrange over top of pie in a spoke pattern, with halves slightly overlapping. Position oven rack 3 to 4 inches from bottom of oven; place pie on rack. Bake just until filling is slightly puffed and set in the middle and crust is golden brown, 40 to 45 minutes, shielding pie with aluminum foil halfway through baking time. Transfer to a wire rack. Cool completely, 2 to 3 hours.