Roll out and arrange pie dough with decorative edge. Place unbaked pie shell in freezer for one hour to firm. Preheat oven to 350 degrees and lower oven rack to lowest position. Brush pie crust edges lightly with egg wash. Use a piece of parchment paper to gently line pie crust. Fill with pie weights and bake for 10 minutes. Then remove pie weights and bake for another 10 minutes. If pie crust starts to bubble, press back down gently with a spoon. Remove pie crust and set aside.
Preheat oven to 375 degrees. In a medium bowl, combine butter and sugar and mix well. Stir in corn syrup, eggs, pecans, rum, vanilla extract and salt. Pour pecan mixture into partially baked pie crust.
Arrange additional pecans in a circular pattern on top of pie. Place pie on baking sheet and bake on lower rack in oven for 10 minutes. Then lower oven temperature to 350 degrees and bake for an additional 25 minutes or until set. Remove from oven and let cool.