Preheat the oven to 350 degrees Fahrenheit. Use a small amount of butter to grease the bottom of a 8-inch springform pan, then dust with flour.

Prepare the topping by combining sliced almonds, butter, sugar, and cinnamon in a mini-food processor and pulsing until the almonds are chopped into very small pieces (about 6-8 pulses). Set aside.

Melt the butter in a microwave-safe container, such as a glass measuring cup, then set aside to cool slightly. Peel apple and chop into roughly 1/4-inch dice. Combine the dry ingredients for the cake in a large bowl (flour, almond flour, sugar, cinnamon, salt, and baking powder). In a smaller bowl, whisk together eggs and vanilla extract.

Pour the slightly-cooled butter slowly into the smaller bowl as you whisk. Stir wet ingredients into dry ingredients until just combined, then stir in chopped apples. The batter will be very thick, almost like cookie batter. Pour into the springform pan and spread evenly. Sprinkle the almond crumb topping over the top. Bake 35-40 min, until a cake tester or toothpick comes out almost clean and the top is nicely browned. Let cool on a rack. Cut gently around the edges of the springform pan before unmolding, then slice and serve! 

This cake will keep well for several days, as the almond flour helps it maintain moisture. Store at room temperature, covered with foil, or in an airtight container.