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.
Add in the eggs, salt and vanilla and whisk until combined.
Lastly, add in the chopped pecans and stir.
Pour the filling into a prepared pie dish.
Brush egg yolk on the crust of the pie. Don't be shy, brush it on really good!
Bake for 20 minutes at 400 degrees.
Cover the crust with tinfoil after it starts to brown.
Turn the oven to 325 degrees and bake for another hour or until the center of the pie is like a Jello texture.
Let the pie cool for a few hours, even overnight. If it's very jiggly, it needs to sit before serving.