Preheat the oven to 350ºF and lightly grease a 11"x7" baking dish, (4-5" deep).
Whisk together the almond flour, tapioca starch, cinnamon, sea salt, baking powder, and baking soda until no lumps remain. Stir in the lemon zest, then add the maple syrup, eggs, melted ghee/butter/avocado oil, and vanilla extract. Mix until just combined, then stir in the apples.
Pour the cake batter into the prepared baking dish. In a small bowl stir together the ingredients for the streusel topping until combined. Using your hands, crumble the streusel topping evenly over the cake.
Bake the cake until puffed and toothpick inserted into the center comes out clean, or with moist crumbs, 40-50 minutes.
Remove the cake from the oven and let it cool to room temperature on a cooling rack before frosting it.
For the frosting, start by placing the butter in a small saucepan over medium heat. Cook swirling it around the bottom until it smells toasty and has browned, 2-3 minutes, (skip this step if using ghee or avocado oil). Add it to the sifted powdered sugar along with the maple syrup, pinch of salt, and vanilla extract.
Stir to combine, then drizzle it evenly over the cake. Serve within the first day for the best texture, although we enjoyed this cake for 3 days before it started to be a bit dry.
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Notes
Baking powder can have all sorts of additives, and isn’t always gluten free or paleo. To be safe, you can make your own by mixing together 1 part baking soda to 2 parts cream of tartar, and use the mixture right away.You can sub in regular powdered sugar for the powdered maple sugar. The frosting will have less maple flavor, but I've tried it that way and it's delicious as well as more accessible.