Heat oven to 350°F. Grease a 9×5-inch loaf pan and line with a parchment sling.
Whisk flour, baking soda, baking powder, salt, and cinnamon in a medium bowl.
Mash bananas in a large bowl. Whisk in granulated sugar and brown sugar until glossy.
Add yogurt, heavy cream, applesauce, and vanilla. Whisk until smooth.
Stream in melted butter while whisking to combine.
Fold dry ingredients into the wet mixture just until no dry streaks remain.
Fold in walnuts, if using. Scrape batter into the prepared pan and smooth the top.
Bake 55–65 minutes, until a tester comes out clean or with a few moist crumbs.
Cool in pan 15 minutes. Lift out, transfer to a rack, and cool completely before slicing.