Preheat the oven to 350°F. Lightly grease 3 donut pans with cooking spray or butter. (NOTE: Most donut pans make 6 donuts. If you only have one pan, you can bake these in batches!)
Place brown sugar, granulated sugar and 6 tablespoons of butter in the bowl of a stand mixer, fitted with a paddle attachment. Cream together until light and fluffy, about 3-4 minutes. Meanwhile, stir together gluten free all purpose flour, cassava flour, baking powder, baking soda, salt, ½ teaspoon ground cinnamon, nutmeg, ginger, and cloves. Set aside. Measure the milk and vanilla extract. Set aside.
Once the butter and sugar is creamed together, add the eggs, one at a time, scraping down the bowl between each addition. Next, add ⅓ of the flour mixture, and mix on medium speed until just combined. Stop the mixer, scrape down the bowl, and add ½ of the milk mixture. Repeat the process with another ⅓ of the flour mixture, remaining milk mixture, and remaining flour mixture. Scrape down the bowl one more time, and beat the mixture on medium speed for 1-2 more minutes, or until fluffy.
While the donut batter is mixing, stir together diced apples, lemon juice and zest, and remaining butter and ground cinnamon. Place the mixture into a microwave safe bowl, and microwave on high for 90 seconds. Once the donut batter is made, gently fold the apple mixture into the donut batter.
Place the batter in a large zip top bag or piping bag, and cut about a 1-inch hole at the end. Divide evenly among the donut pan, placing about ⅓ of a cup of batter into each donut mold. Place the donuts in the oven, and bake for about 14-16 minutes rotating the pan halfway through baking. Once the donuts are done baking, remove from the oven, and immediately turn out onto a wire cooling rack.
While the donuts bake, make the crumble topping. Stir together the gluten free all purpose flour, brown sugar, butter, cinnamon, and salt in a small bowl. Sprinkle evenly onto a small, parchment-lined baking sheet. Bake for 6-8 minutes, rotating the pan halfway through baking, until the mixture is lightly browned and bubbly. Remove from the oven, and let cool. Once cool enough to handle, crumble the mixture by hand, into pea sized pieces. Place in a bowl, and set aside.
Once the donuts are baked and cooled completely, make the glaze. In a small bowl whisk together the powdered sugar, butter, milk, vanilla extract, cinnamon, and salt, until well combined. Gently dip the top of each donut into the glaze, and immediately dip into the crumb topping mixture. Replace donuts onto the wire cooling rack to allow any excess glaze to drip.