Fit the unbaked pie crust into a 9-inch deep dish pie plate, pressing it gently into the bottom and up the sides. Crimp or flute the edges as desired. Chill the crust in the refrigerator for at least 15 minutes while you prepare the fillings.
Preheat your oven to 350°F. In a large mixing bowl, whisk together the pumpkin puree, 2 eggs, granulated sugar, and 1/4 cup brown sugar until smooth. Add the pumpkin pie spice and 1/4 teaspoon salt, and whisk again to combine.
Pour in the evaporated milk and stir just until the mixture is uniform. Avoid over-whisking to prevent cracking. Set the bowl aside while you make the pecan layer.
In a separate bowl, whisk together the remaining 3 eggs, corn syrup, 1/2 cup brown sugar, melted butter, vanilla extract, and remaining 1/4 teaspoon salt until fully combined and glossy. Stir in the pecan halves until evenly coated.
Remove the chilled crust from the refrigerator. Pour the pumpkin filling into the crust first, spreading it into an even layer. Slowly and evenly spoon the pecan mixture over the top, distributing the pecans across the whole surface.
Gently tap the pie plate on the counter a few times to settle the layers and release any large air bubbles.
Place the pie on a rimmed baking sheet and set it on the center rack of the oven. Cover the edges with a pie crust shield or foil to prevent over-browning.
Bake for 55 to 65 minutes, removing the shield for the final 15 minutes so the pecan topping can turn deep golden brown. The pie is done when the pumpkin layer is set around the edges but still has a slight jiggle in the center, and the pecan topping looks caramelized.
Transfer the pie to a wire cooling rack and let it cool at room temperature for at least 2 hours. For the cleanest slices, refrigerate the fully cooled pie for at least 1 hour, or overnight, before cutting.
Slice with a sharp knife wiped clean between cuts for the neatest layers. Serve with fresh whipped cream, vanilla ice cream, or caramel sauce if desired.