Preheat an oven to 350ºF. Line a 9x5-inch loaf pan with parchment paper so that the paper hangs over the edges and spray with nonstick spray.
Brown the butter. Melt the butter in a small saucepan over low heat and cook, swirling regularly, until light brown and nutty smelling. Remove from the heat and cool slightly.
Combine the dry ingredients. In a small bowl, whisk together the flour, baking soda, and salt. Set aside.
Combine the wet ingredients. Combine the mashed banana and sugars together in a medium mixing bowl. Add the eggs and skyr/yogurt and whisk together until smooth.
Finish the batter. Add the flour to the banana mixture and fold together. Add the browned butter and fold until no streaks of flour or butter remain. Fold in the chocolate and walnuts (if using) and pour the batter into the prepared baking pan. Top with banana slices and turbinado sugar, if desired.
Bake. Bake for 60-65 minutes, or until a cake tester comes out clean. Cool in the pan for 5 minutes, then use he parchment paper to lift the banana bread from the pan. Cool before slicing.