In a small saucepan set over medium heat, brown the butter. Stir the butter occasionally until it turns amber in color and develops little brown specks.
Pour 113g of the brown butter out into a small heat-safe bowl and place it into the freezer for 5 minutes to cool off.
Maple Pecan Caramel Topping
Add the maple syrup, brown sugar and cinnamon to the saucepan with the remaining brown butter. Put the mixture back over the heat, bring it to a simmer, then remove it from the heat.
Preheat the oven to 350°F / 175°C. Butter and line an 8" cake pan* with parchment paper.
Spread the pecans into an even layer at the bottom of the cake pan, then pour the maple caramel over the pecans, stirring as needed to make sure all of the pecans are coated in the caramel.
Banana Sheet Cake
In a medium sized mixing bowl, mash the banana to your desired consistency.
Whisk in the brown sugar and 113g (½ c.) of the cooled brown butter.
Add in both eggs, the vanilla, and sour cream. Whisk vigorously until the mixture is well combined.
Add in the flour, baking powder, salt, and cinnamon. Whisk together just until no flour streaks remain.
Pour the cake batter into the prepared cake pan. Bake for 40-50 minutes, or until a toothpick inserted in the center of the cake comes out clean.
Let the cake sit in the pan for at least 20 minutes, then invert it onto a serving platter and carefully peel off the parchment paper. Wait for the cake to mostly cool off before slicing, then enjoy!