Preheat the oven to 350 degrees F. Butter a 10-by-15-inch rimmed baking sheet. Line the bottom with parchment paper and butter the parchment. Dust the pan with flour and tap out the excess. Set aside.
Cream the butter and sugar in a mixer on medium-high speed until light and fluffy, about 2 minutes. In a medium bowl, whisk together the flour, almond flour, baking powder and salt. Add the dry ingredients to the mixer and beat until combined, scraping down the sides of the bowl as needed. Lower the speed to medium and beat in the eggs one at a time, beating until the batter is smooth and fluffy. Beat in the vanilla and almond extract.
Spread the batter in the prepared baking pan with a small offset spatula, spreading until it forms an even layer. Bake until golden brown and a toothpick inserted in the center comes out clean, 10 to 15 minutes. Let cool completely on a rack.
To assemble, unmold the cake by releasing the edges of the cake using an offset spatula, then flipping the pan over to release the cake onto a cutting board; you may need to tap the pan to help release the cake. Cut the cake in half crosswise with a serrated knife to make 2 pieces, each approximately 5 by 7 1/2 inches. Spread the jam over one of the pieces with a small offset spatula or butter knife. Top with the other cake half, making a sandwich. Trim the edges on all sides so they're even. Spread the chocolate frosting on top. Trim the edges again to neaten them. Sprinkle the nonpereils over the frosting. Cut into 30 pieces, cutting across the short side 4 times (to make 5 rows) and across the long side 5 times (to make 6 rows).