Preheat oven to 325°F. Position a rack in the center of the oven.
If your pie pastry is not already fitted, fit the unbaked 9-inch deep-dish pie pastry into a 9-inch deep-dish pie plate and set aside.
In a large mixer bowl, beat the 2 large eggs on high speed until foamy and pale in color.
Add 1/2 cup all-purpose flour, 1/2 cup granulated sugar, 1/2 cup packed brown sugar, and 1 teaspoon vanilla extract to the eggs. Beat on medium speed until combined, scraping the bowl as needed.
Add the 3/4 cup softened butter to the mixture and beat until fully incorporated and the filling is thick and uniform.
Stir in 1 cup semi‑sweet chocolate chips and 1 cup chopped pecans or walnuts until evenly distributed.
Spoon the filling into the prepared pie shell and smooth the top. Place the pie on a baking sheet and bake 55 to 60 minutes, or until a knife inserted halfway between the edge and the center comes out clean. If the crust is browning too quickly, tent the pie loosely with foil for the last 10–15 minutes of baking.
Remove the pie from the oven and cool on a wire rack. Serve warm or at room temperature.