This cozy cake delivers warmth in every bite with its nutty depth and crispy crumble topping. Perfect for fall gatherings or a comforting afternoon treat.
In a light-colored saucepan, melt 1/2 cup of butter over medium heat. Continue cooking, swirling occasionally, until the butter turns golden brown and has a rich nutty aroma, about 5 minutes. Pour it into a large bowl and let it cool for 10 minutes.
Add the granulated sugar to the brown butter and whisk until combined. Add the eggs one at a time, whisking well after each. Stir in the vanilla extract.
In a separate bowl, whisk together 1 1/2 cups flour, baking powder, 1/2 tsp cinnamon, and salt. Add the dry ingredients to the brown butter mixture in two additions, alternating with the sour cream, stirring gently until just combined. Fold in the diced apples.
Preheat your oven to 350F. Grease a 9-inch round cake pan or 8x8 inch square pan and line the bottom with parchment paper. Pour the batter into the prepared pan and spread it evenly.
Make the crumble topping by combining 1/2 cup flour, brown sugar, oats, and 1/2 tsp cinnamon in a bowl. Add the cold cubed butter and use your fingers to pinch and rub everything together until you have a mixture of coarse, chunky crumbs.
Scatter the crumble topping evenly over the cake batter. Bake for 45 to 50 minutes, until the crumble is deeply golden and a toothpick inserted in the center of the cake comes out clean.
Let the cake cool in the pan for 20 minutes before slicing. Serve warm or at room temperature.