Preheat oven to 350°F and line a sheet pan with parchment paper.
Roll out one half (see Note) of the prepared pie dough on a lightly floured surface, into a rough 15-inch circle. Transfer to a 9-inch pie dish and trim edges to a 1-inch overhang. Tuck overhang under and use your thumb and finger to create a crimped edge. Place pie shell on the prepared sheet pan.
In bowl of a stand mixer fitted with a whisk attachment, or in a bowl with a hand mixer, combine the eggs, corn syrup, brown sugar, melted butter, and vanilla extract. Mix on medium high speed until well combined. Stir in the pecans.
Gently pour the mixture into the prepared pie shell. Bake until the edges are completely set and a knife inserted into the center comes out clean, about 45-55 minutes. Let cool before serving, serve warm or at room temperature with whipped cream, if desired.