Step 1

Preheat oven to 350°. Butter a 9”-diameter cake pan and line bottom with a round of parchment paper; butter parchment.

Step 2

Melt ¾ cup butter in a medium saucepan over medium heat, then cook, stirring often, until butter foams, then browns (do not let burn), 5–8 minutes. Pour into a medium bowl; let cool. Chill brown butter until cold.

Step 3

Fit a clean medium saucepan with thermometer and bring maple syrup to a boil over medium-high heat; cook until thermometer registers 265° (syrup will be thicker and a shade darker). Pour into prepared pan and spread with an offset spatula or a spoon to cover bottom; let cool (syrup will harden as it sits).

Step 4

Whisk almond flour, polenta, baking powder, and salt in a medium bowl. Using an electric mixer on medium-high speed, beat chilled brown butter and ¾ cup sugar until very pale and fluffy, 5–7 minutes. Add eggs 1 at a time, beating to blend between additions. Beat until light and fluffy, about 4 minutes. Reduce speed to low, gradually add dry ingredients, and mix just to combine. Scrape batter into pan; smooth top.

Step 5

Bake until cake is golden brown and pulls away from sides of pan, 50–55 minutes. Transfer pan to a wire rack; let cake cool in pan 20 minutes. Turn out onto rack and let cool completely.

Step 6

Using an electric mixer, beat heavy cream, sour cream, and remaining 1 Tbsp. sugar in a medium bowl until soft peaks form. Serve cake with whipped-cream mixture.

Step 7

Cake can be baked 1 day ahead. Store tightly wrapped at room temperature.