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 1 stick melted unsalted butter, 1 cup packed light brown sugar, 1 large egg, 1 teaspoon vanilla extract, ½ teaspoon almond extract, and ¼ teaspoon kosher salt together in a large bowl with a flexible spatula until smooth and glossy.

Add 1 ¼ cups all-purpose flour and sprinkle with ½ teaspoon baking powder. Stir until a thick batter forms. Transfer to the pan and spread into an even layer.

Beat 6 tablespoons room temperature unsalted butter, ⅓ cup granulated sugar, and ¼ teaspoon kosher salt in the bowl of a stand mixer fitted with the paddle attachment on medium speed until pale and fluffy, 1 to 2 minutes. Scrape down the sides of the bowl with a flexible spatula.

With the mixer on low speed, beat in 1 teaspoon vanilla extract, ½ teaspoon almond extract. Beat in 2 large eggs one at a time, waiting until the first is completely incorporated before adding the second (the mixture will look curdled). Scrape down the sides of the bowl again.

Beat in 1 ¼ cups 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 ½ cup sliced almonds evenly over the top. Press into the frangipane.

Bake until golden brown and the center is puffed, 38 to 42 minutes. Let cool completely, about 2 hours. Dust with powdered sugar. Grasping the excess parchment, lift the slab onto a cutting board and cut into 16 pieces.