Preheat oven to 350 degrees F (175 degrees C).
Roll pie dough in a 9 1/2-inch glass pie dish and crimp the edges. Cover dough in parchment paper and press paper down to line the dough; pour pie weights on top of the parchment paper and spread evenly over the bottom.
Bake in the preheated oven for 20 minutes. Remove parchment paper and pie weights to a bowl. Bake crust until lightly golden and set, about 10 minutes more.
Spread pecans out on a baking sheet. Bake in the oven until lightly toasted, 7 to 8 minutes.
Stir brown sugar, butter, white sugar, corn syrup, flour, milk, bourbon, vanilla extract, and salt together in a saucepan over medium heat; bring to a boil, whisking constantly. Remove from heat and cool for 5 to 10 minutes.
Whisk eggs in a large bowl. Slowly drizzle sugar mixture into eggs, whisking constantly.
Spread pecans out in the bottom of the crust. Pour sugar mixture over nuts and gently stir with a spatula to coat all of the nuts.
Bake pie in the preheated oven until crust is golden brown and pie is set, 40 to 45 minutes. Cool completely.