0.25 cup cold unsalted butter, cubed (for crumble)
0.5 teaspoon ground cinnamon (for crumble)
Instructions
Preheat your oven to 350 degrees Fahrenheit and grease a 9-inch round cake pan or springform pan with butter or oil. In a small bowl, toss the sliced apples with one tablespoon of sugar and one teaspoon of cinnamon, then set them aside so the flavors can meld.
In a separate medium bowl, combine the half cup of flour, brown sugar, and cinnamon for the topping. Use a pastry cutter or your fingers to work the cold, cubed butter into the mixture until it looks like coarse crumbs, then place it in the refrigerator to keep the butter chilled.
In a large mixing bowl, beat the softened butter and the 0.75 cup of granulated sugar together until the mixture is light and fluffy. Add the eggs one at a time, beating well after each addition, and then stir in the alcohol-free vanilla extract.
Whisk together the flour, baking powder, and salt in a small bowl. Gradually add the dry ingredients to the butter mixture, alternating with the milk, and stir until just combined, being careful not to overmix the batter.
Spread the cake batter evenly into the prepared pan. Arrange the cinnamon-coated apple slices over the top of the batter in an even layer. Sprinkle the chilled crumble topping generously over the apples and bake for 45 to 50 minutes, or until a toothpick inserted into the center comes out clean. Let the cake cool for at least 15 minutes before slicing.