1. To make your crumble cake: Preheat your oven to 350°F (180°C). Butter a 9 inch springform pan and line the bottom with parchment paper (butter parchment paper too).
2. To make the crumble topping, combine sugar, flour and chilled butter in a bowl. Stir with a fork or pastry blender until the mixture is crumbly. Let sit in the fridge until ready to use.
3. For the cake: In a medium bowl, sift flour, baking powder, salt and baking soda together.
4. In a separate bowl, beat butter, sugar, and 2 eggs until fluffy, about 2-3 minutes on high speed. Add Greek yogurt and vanilla extract (if using) and continue beating until creamy, for about 1 more minute.
5. Reduce the mixer speed to low, mix in the flour and mix until combined.
6. Transfer the cake batter to the springform pan. Top with sliced peaches, pressing slightly into the cake batter. Sprinkle with 1 teaspoon granulated sugar and sprinkle with the prepared crumble topping.
7. Bake until the peach crumble cake and topping turn golden, and a knife comes out clean in the center, about 40 minutes to 1 hour, depending on your oven. When the crumble cake is done, allow cooling (still in the springform pan) on a wire rack. Once cooled, release the peach crumble cake from the springform pan and transfer to a serving plate. Enjoy your crumble cake with a scoop of ice cream!
