In a small mixing bowl, beat butter with electric mixer on medium speed for 30 seconds. Add sugar; beat until well combined. Add egg; beat well. In small bowl, combine flour, soda, nutmeg, and salt. Add to creamed mixture. Beat on low speed until combined.
Transfer batter to a large bowl. By hand, fold in apples and pecans. Spread in a greased 8x8x2-inch baking pan.
Bake in a 350 degree F oven for about 55 minutes. Cut into 9 squares. Serve warm with Rummy Sauce. Makes 9 servings.
In a small saucepan, melt butter or margarine. Stir in sugar and light cream. Bring just to boiling over medium heat. Reduce heat and cook for 3 minutes, stirring occasionally. Remove from heat. Stir in rum, ground nutmeg and vanilla. Pour over warm pudding. Makes about 1-1/2 cups sauce.