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Step 1
Preheat the oven to 350°F and grease a 9x13-inch baking dish.
Step 2
Make the filling: In a small bowl, mix together the brown sugar, cane sugar, and cinnamon. Set aside.
Step 3
Make the crumble topping: In a medium bowl, mix together the flour, brown sugar, cane sugar, and cinnamon. Add the butter and use a spatula to combine. Mix until there is no dry flour remaining and the mixture is crumbly. Don’t overmix. Set aside.
Step 4
Make the cake: In a large bowl, whisk together the flour, baking powder, baking soda, and salt.
Step 5
In the bowl of a stand mixer, or using an electric mixer, cream the butter. Add sugar and mix to combine. Add the eggs one at a time, beating well after each addition. Mix in the vanilla. Add a quarter of the dry ingredients and mix, then add a third of the yogurt and mix. Repeat until you have added all the yogurt and dry ingredients, ending with the dry ingredients.
Step 6
Evenly spread half the batter at the bottom of the prepared pan. Sprinkle with the filling. Dollop the remaining batter in spoonfuls across the top of the filling and use a spatula or knife to carefully spread it into an even layer. Sprinkle the crumble topping on top.
Step 7
Bake for 45 to 50 minutes, or until a toothpick inserted comes out clean.