Prep the pan and oven: Heat oven to 350°F (175°C). Grease and line an 8- or 9-inch square pan or a 9-inch springform with parchment.
Make the crumble: In a bowl, mix flour, brown sugar, granulated sugar, cinnamon, and salt. Stir in melted butter until clumps form.
Chill while you make the cake.
Prep the apples: Toss diced apples with lemon juice and 1 tablespoon flour. This helps keep them bright and prevents sinking.
Dry ingredients: In a medium bowl, whisk flour, baking powder, baking soda, salt, and cinnamon.
Cream the butter and sugar: In a large bowl, beat softened butter and sugar until light and fluffy, about 2–3 minutes.
Add eggs and vanilla: Beat in eggs one at a time, then mix in vanilla.
Finish the batter: Mix in half the dry ingredients, then the yogurt and milk, then the remaining dry ingredients. Stir just until combined.
Fold in the apples.
Assemble: Spread batter evenly in the pan. Crumble the topping over the batter in pea- to marble-sized chunks.
Bake: Bake 45–55 minutes, until the top is golden and a toothpick in the center comes out mostly clean with a few moist crumbs.
Cool and serve: Let it cool in the pan for 15 minutes. Serve warm or at room temperature.
Optional: dust with powdered sugar or add a scoop of vanilla ice cream.