Brown butter in a small pan over medium heat until it smells nutty and turns golden. Let cool 2 minutes.

Preheat oven to 350°F. Line an 8x8 pan with foil and grease it.

Whisk browned butter and brown sugar until smooth. Add egg and vanilla; mix well.

Stir in flour, baking powder, salt, and cinnamon until just combined.

Fold in apples and nuts if using. Spread batter in pan.

Bake 22–26 minutes until edges set and top is golden. Cool before slicing.