For the frangipane:

2/3 cup sugar

1 cup slivered almonds

Tiny pinch of salt

9 tablespoons unsalted butter, softened

1 large egg

1 large egg yolk

1 1/2 teaspoons all-purpose flour

For the apple filling:

4 Granny Smith apples, peeled, cored, and sliced into 1/2-inch thick wedges

2 tablespoons unsalted    butter, melted

3 tablespoons light brown sugar

1. To prepare the crust, combine the flour, sugar, and salt in the bowl of a mixer fitted with the paddle attachment. Add the chilled butter cubes and mix until the butter is partially broken up, but still very chunky. Add 3 tablespoons of ice water and mix until the dough just comes together. If needed, add additional ice water in very small increments. Gather the dough together, shape it into a disk, and wrap in plastic. Chill for at least 30 minutes.

2. While the dough chills, prepare the frangipane by placing 1/4 cup of the sugar, the almonds, and salt in the bowl of a food processor and process until the almonds are finely ground, about 1 minute. Set aside.

3. Wipe out the bowl of the mixer, add the softened butter and the remaining sugar, and beat on high speed with the paddle attachment until well combined, about 1 minute. Add the pulverized almond mixture and mix on low speed until well combined. Add the egg and then the egg yolk, beating well after each addition. Continue beating the mixture on medium-high speed until light and fluffy, about 3 minutes. Mix in the flour until just combined. Set the frangipane aside.

4. Position a rack in the center of the oven and preheat to 375 degrees.

5. Lightly flour your work surface and roll the chilled dough out into a circle 15 inches in diameter. Transfer the dough to a baking sheet lined with parchment paper. Spread half (1 cup) of the frangipane evenly over the dough, leaving a 2-inch border around the perimeter. Arrange the apples in an even layer over the frangipane. Fold the border of the crust over toward the center of the circle, partially covering the apples. Brush the crust with the melted butter. Sprinkle 2 tablespoons of the brown sugar over the crust, and the remaining tablespoon of sugar over the apples.

6. Bake the crostata for 45 minutes to 1 hour, until the apples are tender and the crust is golden brown. Slide the tart off the pan onto a wire rack, remove the parchment paper, and let cool before slicing into wedges to serve.