Heat oven to 350°F. Line bottom and sides of 9-inch square pan with foil, leaving 1 inch of foil overhanging at 2 opposite sides of pan. In small bowl, stir together butter, 1/2 cup sugar and the flour. Press in bottom and 1/2 inch up sides of foil-lined pan. Bake 20 minutes.
Reduce oven temperature to 300°F. In small bowl, beat egg yolks and 1/4 cup sugar with electric mixer on medium-high speed until thick. Gradually beat in cream, rum and 1/4 teaspoon nutmeg. Pour over baked layer.
Bake 40 to 50 minutes at 300°F until custard is set and knife inserted in center comes out clean. Cool completely, about 1 hour.
Sprinkle tops of bars evenly with 1/2 teaspoon nutmeg. Using foil handles, lift cooled bars from pan to cutting board; remove foil from sides of bars. With sharp knife, cut into 6 rows by 6 rows. Cover; store in refrigerator.