Prepare the Pan: Preheat the oven to 350°F. Line the bottom of a 9-inch springform pan with parchment paper, then generously grease the pan.
Make the Frangipane: Place the room-temperature butter, almond flour, granulated sugar, egg white, salt, and almond extract in a small mixing bowl. Beat on high for 1–2 minutes, until the mixture is smooth. If using a hand mixer, there is no need to clean the beaters before making the cake batter. Combine Dry Ingredients: Whisk the all-purpose flour, almond flour, baking soda, baking powder, and salt together in a bowl. Set the mixture aside.
Cream Butter Sugar: Using a hand mixer or stand mixer, beat the room-temperature butter and granulated sugar for 2–3 minutes, until light and fluffy.
Add Wet Ingredients: Add the eggs, sour cream, vanilla, and almond extract to the butter mixture. Mix on low speed until smooth.
Finish the Batter: Add the dry ingredients to the wet mixture and mix on low until the batter is completely smooth. Avoid overmixing. Scrape down the sides of the bowl with a rubber spatula and check that no pockets of flour remain. Fill the Pan: Transfer the cake batter to the prepared springform pan and smooth the surface into an even layer.
Create the Swirl: Transfer the frangipane to a piping bag or sandwich bag and snip off the corner. Pipe one large, thick swirl over the cake batter. Place the raspberry jam in another piping bag or sandwich bag and pipe it just inside the frangipane swirl. Use a knife or toothpick to gently swirl the frangipane and jam into the cake batter. Add Raspberries Almonds: Wash and dry the fresh raspberries thoroughly. Arrange them over the surface of the batter; they will sink into the cake as it bakes. Sprinkle the sliced almonds evenly over the top.
Bake the Cake: Bake at 350°F for 40–45 minutes. The cake should be set when finished, although the frangipane may still have a slight wobble.
Cool Completely: Allow the cake to cool completely before removing it from the pan.
Release the Cake: Run a knife carefully around the edge of the cake to loosen it from the pan, then remove the outer ring of the springform pan.
Finish Serve: Dust the cooled cake with powdered sugar if desired. Serve it on its own or alongside whipped cream and fresh raspberries.