Fit the pie dough into a deep-dish pie plate, then refrigerate it while preparing the filling. Cold dough keeps the butter firm and helps the crust hold a defined edge during baking.

Combine the granulated sugar, brown sugar, salt, corn syrup, and softened or melted butter in a large bowl, then whisk in the eggs and vanilla. The mixture should look smooth and glossy, with no visible streaks of egg or butter.

Set aside several pecan halves, then fold the remaining pecans into the filling and pour it into the chilled unbaked crust. Place the reserved halves over bare spots and spoon filling over them so they are lightly coated.

Bake at 425 °F for 10 minutes, then reduce the oven to 350 °F and continue baking for about 50 minutes. Halfway through, loosely dome greased foil over the pie without letting it touch the sticky filling, and allow the pecans to float naturally toward the surface.

Cool the pie completely for several hours before cutting, or refrigerate for 1-3 days until serving. The filling firms as it cools, so the slices become much cleaner once the center is fully settled.