Preheat the oven to 400ºF.
Butter a 9-inch cake pan with 1 tablespoon of the butter and lightly flour it.
Beat the eggs until light and frothy. Gradually add 2 cups of the milk and mix well. Add the cornmeal, baking powder, and salt.
Melt the remaining 1 tablespoon butter and combine with the remaining 1/2 cup milk and the rice in a food processor or blender and process to make a paste.
Add the rice mixture to the cornmeal mixture, stirring to mix thoroughly. Pour into the cake pan and bake for about 45 minutes, or until light golden. Let cool for several minutes.
Slice into wedges to serve. The bread can be wrapped in plastic wrap and stored in the refrigerator for up to three days. To reheat, sprinkle with a little water before putting it in the oven.
Yield: 6 to 8 servings