Preheat oven to 350.F. Prepare a 9"-diameter cake pan.
Brown the butter in a pan. Transfer to a bowl and chill until cold.
Bring maple syrup to a boil over medium-high heat. Cook until syrup is 365.F. Pour syrup into prepared pan and spread evenly over bottom.
In a medium bowl, whisk together almond flour, polenta, baking powder, and salt.
In a separate container, cream the brown butter and sugar.
Beat the eggs into the butter one at a time. Continue to beat until fluffy.
Gradually mix the dry ingredients into the wet just to combine. Scrape batter into pan, smoothing top.
Bake until golden brown and pulling away from the sides of the pan.
Cool cake in pan on a rack.