Preheat oven to 375 degrees. Butter a round pan 7 inches in diameter by 4 inches high (or Charlotte mold) and place circle of wax paper on bottom of pan. Pour pumpkin in medium bowl. Heat milk, butter, and sugar in saucepan over low heat stirring constantly. Add to pumpkin along with cornmeal, 1/2 cup at a time, stirring to blend. Add salt.
Separate eggs. Drop yolks into center of the cornmeal mixture. Blend. In a mixing bowl, beat egg whites until stiff. Fold into batter. Add rum if desired. Mix.
Pour batter into prepared pan. Place on middle shelf of oven. Test after 1 hour of baking. Bake longer if needed, testing at 10-minute intervals. Cool 20 minutes before unmolding. Slice. Best eaten warm.