Preheat the oven to 350°F (175°C). Grease a 9x5-inch loaf pan and line it with parchment paper.

Brown the butter in a light-colored skillet over medium heat until foamy and the milk solids toast to a nutty brown. Let cool slightly.

In the same bowl, whisk together the browned butter and granulated sugar until glossy. Add eggs one at a time, whisking until incorporated.

Stir in mashed bananas, yogurt, and vanilla until smooth.

In a separate bowl, sift together flour, baking soda, salt, and cinnamon. Fold dry ingredients into wet in two additions until just combined.

Gently fold in nuts or chocolate chips if using.

Spoon batter into the prepared pan, smooth the top, and slide into the oven.

Bake for 50–60 minutes, or until a toothpick inserted into the center comes out with a few moist crumbs.

Cool in the pan for 15 minutes, then lift out using the parchment and cool completely before slicing.