Place the sliced apples in a large bowl. Combine the white sugar, brown sugar, flour and cinnamon in a small bowl and then sprinkle the mixture over the apples. Toss everything together to coat really well and set the apples aside.
Use a food processor or electric mixer to cream the butter and sugar together until light and fluffy. Add the flour and crushed almonds and process or blend until a soft dough comes together. Press the dough into the bottom and 2-inches up the sides of a 9-inch springform pan. Chill the crust in the refrigerator for at least 10 minutes.