Gather all the ingredients needed to make the apple crumble coffee cake.

Preheat your oven to 350°F (175°C), positioning the oven rack in the center. Generously grease a 9x12-inch baking dish with 2 teaspoons of unsalted butter to ensure easy removal and even baking.

In a medium mixing bowl, whisk together the dry ingredients: all-purpose flour, baking powder, baking soda, and ½ teaspoon of fine sea salt. Once fully combined, set this dry mixture aside.

In another bowl, prepare the crumble topping by mixing together the finely chopped toasted walnuts, ⅓ cup packed light brown sugar, ⅓ cup white sugar, 3 tablespoons melted unsalted butter, ground cinnamon, and ¼ teaspoon salt. Stir until the walnuts and sugars are well coated in butter and set the crumble mixture aside.

In a separate large bowl, beat together 1 cup white sugar and ½ cup room-temperature unsalted butter using a spatula or hand mixer until the mixture becomes smooth and creamy.

Add one egg to the creamed butter and sugar mixture and whisk for 2 to 3 minutes until the texture becomes smooth and slightly lighter.

Add the second egg, whisking again until it’s fully incorporated into the mixture. Stir in the plain yogurt and vanilla extract, whisking until smooth.

Gradually add the dry ingredients into the wet mixture and whisk just until the flour disappears—be careful not to overmix, which can make the cake dense.

Prepare the apples by removing the cores and slicing them into ⅛- to ¼-inch thick pieces. Stack a few slices at a time, cut lengthwise down the center, then dice crosswise into small cubes.

Fold the chopped apples gently into the batter using a spatula, stirring just until evenly combined throughout the mixture.

Pour half of the batter into the prepared baking dish and spread it evenly. Sprinkle half of the crumble mixture evenly over the batter.

Spoon the remaining batter on top in dollops, gently spreading it over the crumble layer while trying not to disturb it too much.

Sprinkle the remaining crumble topping evenly over the surface of the batter and gently press it into the top with your hands or the back of a spoon to help it adhere.

Bake the coffee cake in the preheated oven on the center rack for about 40 minutes, or until a toothpick or skewer inserted into the center comes out clean, indicating it's fully baked.

Let the cake cool in the baking dish at room temperature for about 30 minutes before slicing and serving to allow the flavors to settle and the structure to firm up.