Preheat oven to 350°F and grease a 9x13 inch baking dish.
Toss sliced apples with granulated sugar, brown sugar, 1/4 cup flour, 1 teaspoon cinnamon, nutmeg, 1/4 teaspoon salt, lemon juice, and vanilla in a large bowl until well coated.
Spread apple mixture evenly in the prepared baking dish.
Combine topping ingredients: In a separate bowl, mix 2 cups flour, 1 1/2 cups sugar, baking powder, 1 teaspoon cinnamon, and 3/4 teaspoon salt.
Stir in beaten eggs until mixture is crumbly, then drizzle in melted butter and mix until just combined.
Sprinkle topping evenly over apples. Some clumps are fine and will create golden peaks.
Bake for 45-55 minutes until topping is golden brown and filling is bubbling around edges.
Rest for 10 minutes before serving to allow filling to thicken slightly.