Preheat the oven to 325 degrees F. Roll out the dough into a 12-inch round on a lightly floured surface. Ease the dough into a 9 1/2-inch deep-dish pie plate; fold the overhanging dough under itself and crimp the edges.
In a large mixing bowl, whisk the brown sugar, granulated sugar and eggs until creamy. Add the chopped pecans, melted butter, milk, flour and vanilla extract and stir to combine. Pour the mixture into the pie shell. Arrange the pecan halves on top of the pie in a circular pattern.
Bake the pie for about 55 minutes. Check for doneness by shaking the pan slightly: The pie should be firm with a slight jiggle in the center. Let cool on a rack, about 2 hours. Serve topped with ice cream or whipped cream.