1 cup granulated sugar
1 cup all-purpose flour
1 tsp. baking powder
5 Tbsp. cold unsalted butter, cut into a few pieces
1 tsp. vanilla extract
1 large egg, lightly beaten
3 large Granny Smith apples, peeled, cored, and sliced very thinly
3 Tbsp. granulated sugar
3 Tbsp. unsalted butter, melted and cooled slightly
1 tsp. ground cinnamon
1 large egg
Preheat oven to 350. Butter and flour a 9-inch springform pan.
In the bowl of a food processor fitted with the steel blade attachment, combine the sugar, flour, and baking powder. Pulse to mix. Add the butter, and pulse until no large lumps remain. Add the vanilla and the egg, and blend well, until it resembles cornmeal. Dump it into the prepared springform pan. Nudge it around with your fingertips to distribute it evenly, and then gently press it along the bottom of the pan. You?re not trying to really tamp it down; you just want to compact it a little. At the edges, let it curve up ever so slightly, like a tart shell with a very low, subtle rim. Arrange the apple slices over the base in a tight circular pattern. It may seem as though you have too many apple slices to fit, but keep going. Really squeeze them in. Slide the pan into the oven, and bake for 45 minutes.
Meanwhile, make the topping. Combine the ingredients in a small bowl, and whisk to blend well. After the cake has baked for 45 minutes, remove it from the oven, and spoon the topping evenly over it. Bake for another 25 minutes or so, until the topping looks set. Transfer the pan to a wire rack, and cool for 20 minutes. Then run a thin knife around the edge to release any areas that may have stuck, and remove the sides of the pan. Cool completely before serving.
Note: This cake is even better on the second day. So if you can, make it a day ahead: just wrap it in plastic wrap and leave it at room temperature until you?re ready to eat it.