To brown the butter, place in a small saucepan over medium heat. Once the butter melts, continuously whisk it until little brown bits appear on the bottom of the pan.
Remove the pan from the heat and continue to stir for about 30 seconds. Let cool slightly.
Preheat the oven to 325°.
Spray a 5" x 9" loaf pan with nonstick spray.
In a large bowl, whisk together the browned butter and brown sugar.
Once it is combined, stir in the coconut milk, bananas, eggs, and vanilla extract.
In a small bowl, whisk together the flour, baking soda, salt, and cinnamon.
Add the dry ingredients to the wet and mix them with a large spoon until just combined.
Pour the batter into the greased loaf pan. Bake the bread for 60 minutes, rotating the pan once during the cooking time. Check doneness with a wooden pick inserted into the center. It should come out clean or have a few crumbs on it.
Remove the bread from the oven and let cool in the loaf pan for 20 minutes. Gently remove the bread and place on a cutting board to cool completely before cutting.