Adjust an oven rack to the lower third position in the oven. Preheat the oven to 400°F (204°C).
Roll out the pie dough to about 12 inches in diameter, transfer to a 9-inch pie plate, gently fit it in the dish, and trim any excess dough from the edges. Place the pie plate in the refrigerator and allow the dough to chill for 15 to 20 minutes while the oven is preheating.
Once the oven is preheated, remove the pie plate from the refrigerator, decorate the edges, and line the dough with parchment paper or foil, making sure to cover the bottom and the sides. Fill with pie weights, making sure to press them up against the sides as well.
Bake in the lower third of the oven with the pie weights for 15 minutes or until the edges of the crust start to lightly brown. Remove from the oven, carefully remove the parchment paper (or foil) and the pie weights. Return to the oven and bake for an additional 6 to 8 minutes or until the bottom of the crust looks dry. Remove from the oven. Reduce the oven temperature to 375°F (190°C).
In a large mixing, whisk together the beaten eggs, light corn syrup, brown sugar, and granulated sugar until fully combined. Whisk in the melted butter and vanilla extract until well combined, then stir in the chopped pecans.
Pour the pecan pie filling into the warm pre-baked crust. Cover the edges of the pie with foil or a pie crust shield if desired (I prefer to add mine at this point, but you can wait until the edges start to brown more then add one).
Return the pie to the oven (in the lower third of the oven again) and bake at 375°F for 40 to 45 minutes or until the top of the pie is set. If the pie begins to brown too much before it's finished baking, tent with foil.
Remove the pie from the oven and allow to cool completely at room temperature. Then slice and enjoy or cover tightly and refrigerate until ready to serve.