Preheat the oven to 350° F. Butter a 9"x12" baking dish. Whisk flour, baking powder, baking soda, and sea salt together in a bowl. Set dry ingredients aside. Crumble mixture: Combine walnuts, brown sugar, white sugar, melted butter, cinnamon, and salt in a bowl until walnuts and sugars are thoroughly coated with butter; set crumble mixture aside. Beat white sugar and butter together in a separate bowl with a spatula until well blended. Whisk in egg until mixture is smooth, two to three minutes. Whisk in the second egg until thoroughly incorporated. Add yogurt and vanilla and whisk together. Add flour mixture to yogurt mixture; whisk just until flour disappears. Do not overmix. Remove and discard cores from apples. Cut apples into 1/8- to 1/4-inch slices. Stack a few slices. Cut down the centre, lengthwise, then dice, crosswise, into cubes. Fold apples into cake batter with a spatula until just combined. Spread half the batter into the prepared baking dish. Evenly scatter half crumble mixture over top. Dollop remaining half batter on top, spreading carefully to evenly distribute, trying not to disturb the crumbs. Top with remaining crumble mixture; press crumbs into the batter very gently. Bake in the centre of the preheated oven until a toothpick or bamboo skewer inserted into the centre comes out clean, about 40 minutes. Cool to room temperature before slicing and serving, about 30 minutes. Yields eight servings.