FOR THE TOPPING: Whisk sugars, cinnamon, salt, and butter in medium bowl to combine. Add flour and stir until mixture resembles thick, cohesive dough; set aside to cool to room temperature.
Using both hands, break apart the crumb topping, rolling the broken dough between your thumb and forefinger to form crumbs about the size of large peas. Continue until all the dough has been broken down into crumbs. In a separate small bowl, take about 1 cup of the topping and mix it with the chopped apple. Set aside both bowls.
FOR THE CAKE: Adjust oven rack to upper-middle position and heat oven to 325 degrees F. Cut a 16-inch length parchment paper and fold lengthwise to 7-inch width. Spray an 8-inch square baking dish with nonstick cooking spray and fit the parchment into dish, pushing it into corners and up sides; allow excess to overhang edges of dish. This allows you to easily remove the cake from the pan once it’s baked.
In a large bowl using a hand mixer, mix flour, sugar, baking soda, and salt on low speed to combine. Add butter to the dry ingredients one piece at a time; continue beating until mixture resembles moist crumbs, with no visible butter chunks remaining, about 1 to 2 minutes. Add egg, yolk, vanilla, and buttermilk; beat on medium-high speed until light and fluffy, about 1 minute, scraping once if necessary.
Pour about half of the cake batter into the prepared baking pan. Sprinkle the 1 cup of crumb topping that has been mixed with the chopped apple on top of the cake batter. Pour remaining cake batter on top, and using a rubber spatula or offset spatula, spread batter into an even layer. Sprinkle remaining pea-sized pieces of crumb topping evenly over the cake batter beginning with edges and then working toward center.
Bake until crumbs are golden and wooden skewer or toothpick inserted into center of cake comes out clean, 40 to 50 minutes. Cool on wire rack at least 30 minutes. Remove cake from pan by lifting parchment overhang.
This recipe can be easily doubled and baked in a 13 x 9-inch baking dish. If doubling, increase the baking time to about 45 minutes. Cooled leftovers can be wrapped in plastic wrap and stored at room temperature for up to 2 days.Adapted from America's Test Kitchen
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