Bananas Foster Loaf Cake

1. Position a rack in the center of the oven and preheat to 325°. Grease a 5-by-9-inch loaf pan. Trim both ends off each of 3 bananas so the bananas will fit crosswise in the pan. Peel the ends and the long pieces and halve the long ones lengthwise; transfer to a plate.
2. In a large, heavy skillet, bring ¼ cup sugar and 2 tablespoons water to a boil, without stirring. Cook until the water evaporates and the mixture just starts turning amber. Remove from the heat and swirl in the butter with a fork. Add the banana pieces cut side down and cook over low heat for 1 minute; then transfer the banana pieces to the prepared loaf pan, arranging them crosswise, cut side down. Drizzle the remaining caramel on top.
3. Transfer 1 cup of the banana ends (add more banana if necessary to equal 1 cup) to a medium bowl; mash with the remaining ½ cup sugar. Beat in the egg, egg white and vanilla.
4. In a large bowl, whisk the flour with the baking powder, cinnamon and salt. Add the banana mixture and oil and whisk until blended. Scrape the batter over the bananas in the pan and bake until a toothpick inserted in the center comes out dry, 50 to 55 minutes. Let cool on a rack for 10 minutes and then invert onto a serving platter and let cool completely.