Place a rack in the center of the oven and preheat to 325 degrees F. Cut the butter into small chunks and place in a large mixing bowl along with the sugar and brown sugar. Use an electric mixer to beat together the butter and sugar for a few minutes. Make sure the butter is fully integrated into the sugar and the mixture becomes small, even sized crumbs.
Add the eggs and applesauce to the bowl and continue to mix till smooth.
In a small bowl, mash the bananas with a fork till smooth. Add the mashed bananas, Greek yogurt, and vanilla to the bowl. Use a spatula to stir the mixture till smooth.
In a medium bowl, sift together the flour, baking soda, cinnamon, salt, cloves and nutmeg. Fold the dry ingredients into the wet to make a thick batter. Don't over mix-- a few lumps are okay.
Fold in the chopped walnuts.
Grease two loaf pans with nonstick cooking oil spray. Divide the batter evenly between the two pans.
Bake the banana bread for 45-55 minutes, turning once halfway through baking, till the top is golden brown and a toothpick inserted into the center of the loaf comes out clean. If the top of the bread browns faster than it bakes, cover with foil for the remainder of baking time.
Let the loaves cool for 10 minutes in their pans, then put them on a wire rack to cool completely.
Serve warm... with tea, perhaps, or a pat of melty butter. This bread is so comforting, a wonderful baked treat to have on hand for unexpected guests. Wrap in plastic wrap or foil to keep moist; store in the refrigerator if you will be keeping it longer than a few days.