Here is a recipe for Kahlua brownies, I would just substitute rum and it should work just fine.Kahlua Fudge Brownies

Recipe By : Concord Hospital Admitting Cookbook - Concord, NH

•1 1/2 cups flour -- sifted
•1/2 teaspoon baking powder
•1/2 teaspoon salt
•2/3 cup butter
•3 squares unsweetened baking chocolate
•3 large eggs
•2 cups sugar
•1/4 cup + 1 Tb Kahlua
•3/4 cup walnuts -- chopped Grease a 9" square pan. Preheat oven to 350F. Sift flour, baking powder, and salt together. Melt butter and chocolate together over low heat. Beat eggs and sugar until light. Add flour mixture, chocolate mixture and 1/4 cup Kahlua. Blend well. Stir in nuts. Bake 30 minutes or until done. Cool in pan. Brush with remain