Place a rack in the upper-middle position of the oven. Preheat oven to 325°F.
In a bowl, combine white sugar, brown sugar, salt and cinnamon, mixing well with your fingers until there are no lumps. Add melted butter and stir until smooth. Stir in cake flour until fully combined. Set aside at room temperature, covered with plastic wrap, to allow the gluten to relax, 10-15 minutes.
In work bowl of a standing mixer, combine flour, sugar, salt and baking soda using the paddle. (If you don't have a stand mixer, whisk together in a large bowl.) With the mixer running on medium-low, add the butter 1 tablespoon at a time, waiting until each piece breaks down before adding the next. Continue mixing until it has a uniform sandy texture. (If working by hand, cut butter in with pastry cutter until very fine.).
Add the vanilla, buttermilk, egg and egg yolk. Run mixer on medium-high until batter is smooth and thick, at least 1 minute, or use a handheld electric mixer. The batter will be very thick, almost like frosting.
Spray an 8"-square baking pan with non-stick spray. Cut a piece of parchment paper 16" by 7 1/2", and lay it into the pan, allowing 2" to overhang each side. Spread the batter into the prepared pan.
Break the crumb mixture into pieces the size of large peas or small pebbles. Spread crumbs around the outer edge of the pan first, then evenly fill in the center.
Place pan in preheated oven for 35-40 minutes, or until a toothpick inserted in the center of the pan comes out clean. Cool cake in pan 30 minutes. Dust top with powdered sugar, then remove cake from pan using parchment sling. Cut into 16 2" squares.