Preheat the oven to 400 degrees.
Brown the butter on the stovetop until it turns a golden brown.
Let it cool a bit and add in the rum.
In a bowl, whisk together brown sugar and corn syrup.
Add in the browned butter and rum.
Then add in the eggs, salt and vanilla and whisk until combined.
Lastly, add in the chopped pecans and stir.
Pour the filling into the pie dish.
Brush egg yolk on the crust of the pie.
Bake for 20 minutes at 400 degrees.
Turn the oven to 325 and bake for 30 minutes or until the center of the pie is like a Jello texture. Do not over bake!
During the baking process I had to take the pie out and wrap foil around the crust so it wouldn't burn. It worked perfectly to protect the crust while the filling baked a little longer.