Mix Wet Ingredients: Add the brown sugar to the warm browned butter and stir until it is fully integrated. Mix in the eggs and vanilla until smooth.
Combine & Bake: Add the flour, baking powder, and salt to the wet ingredients. Stir just until combined. Fold the shredded sweetened coconut into the batter, then transfer the mixture to the prepared baking dish and spread it in an even layer.
Bake: Bake for 40-45 minutes. For the last 10 minutes of baking, cover the dish with aluminum foil to prevent the top from browning too quickly. Let the bars cool completely in the dish before slicing.