4 tbsp. butter, at room temperature
1/2 cups brown sugar
1/2 tsp. cinnamon
1 small lemon
12 ripe figs
6 tbsp. butter
1 cup almond flour
2/3 cups granulated sugar
4 cold eggs
1 tsp. vanilla extract
1/8 tsp. salt
Crème Fraîche, optional
Position a rack in the lowest part of the oven and preheat the oven to 350˚F. Grease the bottom and sides of a nine-by-two-inch round cake pan and line the bottom with a circle of parchment paper. Press and smooth the paper to adhere it to the pan.
Use the back of a spoon to smear the 4 tablespoons of butter topping all over the parchment. Mix the brown sugar with the cinnamon and dump it into the pan. Spread it evenly with the back of the spoon.
Use a micro plane zester to grate the zest of the lemon over the brown sugar. Cut the lemon and squeeze enough juice to measure 1 tablespoon. Drizzle the tablespoon of juice evenly over the brown sugar.
Stem and halve the figs. Arrange them cut side down, close together but not overlapping, to cover most of the brown sugar layer and set aside.
Heat the butter in a small pot until melted and bubbling and let it bubble for about 30 seconds. Turn the heat off now—but be ready to return the pot to the heat the moment you start to whip the eggs later. Set a four- to five-cup bowl (preferably stainless steel) near the stove to receive the brown butter afterward—the bowl must be large enough to allow you to fold some batter into the butter later.
Whisk the flour and 2 tablespoons of the granulated sugar together thoroughly in a medium-size bowl. Set a medium-mesh strainer or a sifter next to the bowl.
Combine the remaining sugar, eggs, vanilla, and salt in the bowl of the stand mixer and beat with the whisk attachment on high speed, for about three minutes or until the mixture is pale yellow and has increased in volume. You should see well-defined tracks as the whisk spins, but when the whisk is lifted, the mixture should flow and sink into the surface of the remaining eggs rather quickly—don't continue beating all the way to the ribbon stage. (You aren't aiming for a mixture so fluffy that it falls in a thick rope that dissolves slowly on the surface of the batter.)
While the eggs are beating, reheat the butter until it bubbles and continue to cook it, swirling the pot, until it is golden brown and the milk particles suspended in it are reddish brown. Immediately pour the butter into the reserved bowl to stop it from cooking further and burning. (It should remain very hot until you need it.)
When the egg mixture is ready, remove the bowl from the mixer. Sift one-third of the flour over the eggs.
Fold with a large rubber spatula until the flour is almost blended into the batter. Repeat with half of the remaining flour. Sift in the remaining flour and sprinkle in any bits of coarse flour that may not have passed through the strainer or sifter. Fold until blended.
Scrape about one-quarter of the batter over the hot brown butter. Fold until blended. Scrape the buttery batter over the remaining batter and fold until blended. Scrape the batter over the figs in the pan.
Bake 35 to 40 minutes until the cake is golden brown and a toothpick inserted into it comes out clean. The cake will just barely show signs of shrinking from the sides of the pan.
Set the cake on a rack for five minutes. Slide a slim knife or small metal spatula around the edges of the cake to detach it from the pan. Invert the cake onto plate. Peel off the parchment if necessary. Scrape any of the brown sugar syrup left in the pan or on the parchment back onto the top of the cake. Let the cake cool before serving.
Serve plain or with a dollop of whipped crème fraîche.