Prepare Banana Bread. Grease a 2-quart rectangular baking dish. Cube bread; place in dish. Whisk together whole eggs, ½ cup sugar, 2¾ cups milk and cinnamon. Pour mixture over bread cubes. Dot with 2 tablespoons butter. Cover; let stand 30 minutes. Preheat oven to 350°F. Bake, uncovered, for 1 hour or until set in center.
In a saucepan combine ¾ cup sugar and cornstarch. Stir in 3 cups milk. Cook and stir until thickened and bubbly; reduce heat. Cook and stir 2 minutes more. Remove from heat. Slightly beat egg yolks. Gradually stir 1 cup filling into yolks. Add yolk mixture to saucepen. Bring to a boil, stirring constantly; reduce heat. Cook and stir 2 minutes more. Remove from heat. Stir in 1 tablespoon butter and 1 teaspoon vanilla. Spread half of filling over bread pudding. Arrange bananas on top of filling. Top with remaining filling.
For meringue, in a mixing bowl combine egg whites, 1½ teaspoons vanilla and cream of tartar. Beat on medium speed until soft peaks form (tips curl). Add remaining ½ cup sugar, 1 tablespoon at a time, beating on high speed until mixture forms stiff, glossy peaks (tips stand straight). Spread meringue over hot filling, sealing edges. Bake for 15 minutes. Cool for 60 minutes.
Banana Bread: Preheat oven to 350°F. Grease bottom of a 9x5x3-inch loaf pan. Set aside. Beat ½ cup butter and ¾ cup sugar. Add 2 large whole eggs, 2 bananas and 1 teaspoon vanilla. Combine well. Add 2 cups all-purpose flour, 1 teaspoon baking powder and 1 teaspoon cinnamon. Mix until blended. Spoon batter into prepared pan. Bake for 55 to 60 minutes or until a wooden toothpick inserted near the center comes out clean. Cool in pan for 10 minutes. Remove from pan; cool completely.