Slice 4 apricot halves for garnish, if desired; set aside. Chop remaining apricot halves. Place chopped apricots on paper towels to drain thoroughly.
Place four 6-ounce custard cups or individual souffle dishes in a shallow baking pan. Divide the chopped apricots among the cups or dishes.
In a small mixing bowl combine the eggs, milk, sugar, vanilla, and rum flavoring or almond extract. Pour the egg mixture over chopped apricots. Sprinkle with cardamom or nutmeg.
Place the baking pan containing the cups or dishes in the oven. Pour boiling water around cups or dishes in pan to depth of 1 inch.
Bake in a 325 degree F. oven for 30 to 35 minutes or until a knife inserted near the centers comes out clean. Remove cups or dishes from water. Serve custards warm. Garnish with the reserved apricot slices and fresh mint, if desired. Makes 4 servings.