Roughly chop 1 cup of the pecans. Scatter the chopped pecans evenly over the bottom of the par-baked pie crust. Set aside.
In a large mixing bowl, whisk together granulated sugar, brown sugar, corn syrup, eggs, salt, vanilla extract, and the cooled brown butter until smooth and well combined. Pour this mixture over the chopped pecans in the crust.
Arrange the remaining ½ cup pecan halves decoratively over the top of the filling.
Bake at 350°F for 30 minutes. Remove from oven and place a pie crust shield (or a ring of aluminum foil) around the edges to prevent the crust from browning too quickly.
Return to oven and bake for another 15-20 minutes, until the pecan topping is deeply toasted and fragrant and the filling has a slight jiggle in the very center but is set around the edges.
Remove from oven and place on a wire cooling rack. Let cool completely to room temperature before slicing (at least 4 hours, overnight is ideal). The filling will set as it cools.