Preheat the oven to 350°F (175°C) and grease a 9-inch square baking pan.
- In a medium bowl, whisk together the gluten-free flour, almond flour, baking powder, baking soda, salt, cinnamon, and nutmeg.
- In a large mixing bowl, cream the softened butter with brown sugar and granulated sugar until light and fluffy.
- Add eggs one at a time, beating well after each addition. Stir in the vanilla extract.
- Alternately add the dry ingredients and milk to the wet mixture, beginning and ending with the dry. Mix until just combined.
- Toss diced apples and cranberries with lemon juice, then gently fold into the batter.
- Pour the batter into the prepared baking pan and spread evenly.
- Prepare the crumble topping by combining flour, brown sugar, and cinnamon. Cut in the chilled cubed butter until the mixture is crumbly.
- Sprinkle the crumble topping evenly over the cake batter.
- Bake for 45–50 minutes or until a toothpick inserted into the center comes out clean.
- Let the cake cool for 10–15 minutes before slicing and serving.