In a large skillet, melt 2 tablespoons of the butter with the brown sugar. Add the apples and cook over moderately high heat, stirring, until tender and golden, 4 to 5 minutes. Add 1/2 teaspoon of the cinnamon and 1/2 teaspoon of the vanilla and transfer the apples to a plate.

Preheat the oven to 350°F. Grease and flour a 9- x 5- x 4 1/2-inch loaf pan. In a medium bowl, stir together the flour, baking soda, salt, cloves, nutmeg, and the remaining 1/2 teaspoon cinnamon.

In a large bowl, using a handheld electric mixer, beat the remaining stick of butter with the granulated sugar on medium speed until light and fluffy. Add the eggs, 1 at a time, and mix until smooth. Add the mashed bananas, orange juice, and the remaining 1 teaspoon of vanilla and beat until smooth. Add the dry ingredients and beat on low speed until smooth. Using a rubber spatula, fold in the apples.

Scrape the batter into the prepared pan and smooth the surface. Bake for 1 hour and 20 minutes, or until a toothpick inserted in the center comes out clean; cover loosely with foil if the loaf becomes too dark. Let the loaf cool in the pan for 10 minutes before turning it out onto a rack to cool completely.