Beat butter at medium speed with an electric mixer until creamy. Add 1/2 cup sugar, beating well. Add eggs, 1 at a time, beating just until blended after each addition.
Combine flour and next 4 ingredients. Combine milk and 3 tablespoons rum. Add flour mixture to butter mixture alternately with milk mixture, beginning and ending with flour mixture; beat at low speed until blended after each addition. Spoon into greased muffin pans, filling three-fourths full.
Bake at 375° for 20 to 25 minutes or until golden. Remove from pans immediately; place on a wire rack. Combine remaining 2 tablespoons rum and 3 tablespoons sugar in a small saucepan; cook over low heat, stirring constantly, until sugar dissolves. Brush over warm muffins.