In a mixing bowl add eggs and sugar, mix until just combined. Add corn syrup, butter (melted), nutmeg, cinnamon, rum extract, vanilla extract and mix everything together until ingredients are completely combined.
Preheat oven to 350°F.
Pour pecans into the bottom of pie crust and pour filling on top of the pecans.
Place in the oven and bake for 50 minutes.
Halfway through baking, about 25 minutes, check the pie to make sure it is not browning too much. Cover with aluminum foil if this happens and continue baking.
Remove from the oven and let cool completely. I love to top pecan pie with buttered pecan ice cream!