Whether you like figs or not, this cake is a winner. It has the richness and texture of pound cake, but it's made with almond paste, which imparts both flavor and moistness. The figs will sink to the bottom, so don't despair. You can also substitute other fruits, such as plums or nectarines - just think of fruits that pair well with almond flavor, and you can't go wrong. The cake will keep, refrigerated, for up to 3 days if wrapped tightly in plastic wrap. It's sweet and luscious enough to stand on its own, but a dollop of whipped cream couldn't hurt!
Position a rack in the center of the oven, and preheat the oven to 350 degrees F. Butter and flour the sides and bottom of a 9-inch springform pan; set aside.
Place the sugar and almond paste in the bowl of a mixer and beat with the paddle attachment until the mixture is crumbly. Add the butter and beat until the batter is smooth, about 2 minutes on high speed. Add the almond and vanilla extracts, and beat briefly to combine. Add the eggs, one at a time, beating until the mixture is smooth before adding the next egg.
In a separate bowl, whisk together the flour, baking powder, and salt. Add the dry mixture to the bowl with the batter and mix at low speed until just combined. Transfer the batter to the prepared pan.
Place the figs, skin side down, atop the cake (they can overlap slightly). Bake until the cake pulls away from the sides of the pan and a skewer or toothpick inserted into the center of the cake comes out clean, about 70 minutes.
Cool the cake in the pan on a wire rack for 10 minutes, then carefully remove the outer ring to let the cake finish cooling completely. Serve at room temperature, with a dollop of whipped cream, if desired.