Heat the oven to 350°F. Line an 8x8-inch baking pan with 2 sheets of parchment paper, positioning them perpendicular to each other so that the parchment hangs about 2 inches over all 4 sides of the pan to form a sling.

Stir melted unsalted butter, packed light brown sugar, large egg, vanilla extract, almond extract, and kosher salt together in a large bowl with a flexible spatula until smooth and glossy.

Add all-purpose flour and sprinkle with baking powder. Stir until a thick batter forms. Transfer to the pan and spread into an even layer.

Beat room temperature unsalted butter, granulated sugar, and kosher salt in the bowl of a stand mixer fitted with the paddle attachment on medium speed until pale and fluffy, about 1 to 2 minutes. Scrape down the sides of the bowl with a flexible spatula.

With the mixer on low speed, beat in vanilla extract and almond extract. Beat in eggs one at a time, waiting until the first is completely incorporated before adding the second. Scrape down the sides of the bowl again.

Beat in almond flour on low speed until just combined, about 30 seconds. Use the spatula to scrape down the sides of the bowl and finish folding in the flour until combined and smooth.

Spread the mixture over the crust in an even layer. Sprinkle sliced almonds evenly over the top. Press into the frangipane.

Bake until golden brown and the center is puffed, about 38 to 42 minutes. Let cool completely. Dust with powdered sugar and cut into 16 pieces.