Preheat the oven to 350°F and grease a 9x13-inch baking dish.

Make the filling: In a small bowl, mix together the brown sugar, cane sugar, and cinnamon. Set aside.

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.

Make the cake: In a large bowl, whisk together the flour, baking powder, baking soda, and salt.

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.

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.

Bake for 45 to 50 minutes, or until a toothpick inserted comes out clean.