For sauce, combine egg; milk, ( half and half or light cream) and sugar in a heavy small saucepan. Cook and stir over medium heat about 6 minutes or till mixture coats a metal spoon. Remove from heat. Stir in rum. Immediately cool by placing the saucepan in a sink of ice water for 2 minutes, stirring constantly. Pour sauce into a bowl. Cover surface with plastic wrap. Chill at least 1 hour or till serving time.

Step 2

Meanwhile, melt butter in a small saucepan. Stir in brown sugar. Cut bananas in half crosswise, the lengthwise. Arrange, cut side down, in a 2-quart rectangular baking dish. Brush entire surfaces of bananas with lemon juice; sprinkle with coconut. Drizzle with brown sugar mixture.

Step 3

Bake, uncovered in a 450°F oven for 10 minutes or till bananas are barely tender and coconut is light golden. To serve, spoon warm bananas into serving dishes. Ladle sauce over bananas.