Step 1: Preheat and Prep

Preheat your oven to 350°F (175°C). Generously butter a 9×12-inch baking dish and set aside.

Step 2: Mix Dry Ingredients

In a bowl, whisk together the flour, baking powder, baking soda, and salt. Set aside.

Step 3: Make the Crumble

In a separate bowl, combine walnuts, brown sugar, white sugar, melted butter, cinnamon, and salt.
Mix until the walnuts and sugars are well coated in butter. Set aside.

Step 4: Prepare the Wet Ingredients

In a large mixing bowl, cream together the white sugar and room-temperature butter using a spatula or hand mixer until smooth.
Add one egg and whisk until fully blended (2 to 3 minutes), then whisk in the second egg.
Stir in the yogurt and vanilla extract until fully incorporated.

Step 5: Combine Wet and Dry

Gradually add the dry flour mixture to the wet ingredients.
Whisk or stir gently just until the flour disappears—do not overmix.

Step 6: Prep the Apples

Core the apples, slice into thin pieces, and then dice into small cubes.
Fold the diced apples into the cake batter using a spatula.

Step 7: Assemble the Cake

Spread half of the batter evenly into the bottom of the prepared baking dish.
Sprinkle half of the crumble mixture evenly on top.
Add the remaining batter in dollops, then gently spread to cover the crumble without disturbing it too much.
Top with the remaining crumble mixture and press lightly into the surface.

Step 8: Bake

Bake on the center rack for about 40 minutes, or until a toothpick inserted in the center comes out clean.

Step 9: Cool and Serve

Let the cake cool at room temperature for at least 30 minutes before slicing and serving.