Preheat the oven to 350 degrees. Butter and flour the bottom and sides of a 9-inch springform pan, and line the bottom of the pan with parchment paper. Cut the figs in half (or in quarters if large) through the stem. Place them in a small bowl, add 1 tablespoon of the sugar, and toss. Set aside.
Make the frangipane: Combine the butter, egg, almond flour, sugar, all-purpose flour, almond extract and salt in a medium bowl. Using a wooden spoon, stir until the mixture is combined and forms a smooth, paste-like batter. Set aside.
Make the cake batter: Place the butter and remaining ¾ cup sugar in the bowl of a stand mixer. Mix on medium speed for 3 minutes, until light and fluffy. Add the egg, lemon zest, vanilla extract, and almond extract and mix on medium-low speed until combined, scraping down the sides of the bowl with a spatula as necessary. Add the sour cream and mix until just combined.
In a small bowl, whisk together the flour, baking powder, and salt. With the mixer on low, gradually add the dry to ingredients to the wet ingredients and mix until just combined.
Spoon about half the cake batter into the prepared pan and spread it into an even layer. Place small spoonfuls of the frangipane on top, covering as much of the cake as possible, then gently spread the frangipane with a spatula to cover the entire surface of the cake. Finally, place spoonfuls of the remaining cake batter on top of the frangipane and gently spread into an even layer.
Arrange the figs, cut sides up, on the cake in concentric circles. Place the cake on a sheet pan and bake for 60 to 65 minutes, or until the center of the cake is just set. Cool for 20 minutes in the pan, then transfer to a cake plate and serve warm or at room temperature, with whipped cream if desired (recipe follows.)Copyright 2021, Lidey Heuck, All Rights Reserved.