Set the cubed butter on a plate and place it in the freezer for 15 minutes. Fill a cup with ice and water and set aside. Place 1 1/2 of the flour, 1 8 teaspoon of the salt, and 1 tablespoon of the sugar in the bowl of a food processor and pulse to combine. Take the butter out of the freezer and add it to the flour. Pulse the mixture until it looks like wet sand, about 10 seconds. Add 2 to 3 tablespoons of the ice water and pulse until the dough comes together into a ball.

Lightly flour your work surface and place the dough on top. Then lightly flour the top of the dough and roll to about a 10- to 11-inch circle, sprinkling more flour under and on top of the dough as necessary. Gently drape the dough over the rolling pin and transfer it to a 9- or 9 1/2-inch fluted tart pan (ideally one with a removable bottom). Fit the dough into the bottom and up the sides of the pan as evenly as possible and press off excess dough from the fluted rim. Set the tart pan on a baking sheet and place in the refrigerator for 15 minutes.

Preheat the oven to 350degreesF. Peel, core, and quarter the apples and then thinly slice them lengthwise. Place the apples in a large bowl and toss with the lemon juice, the cinnamon, and the remaining 1 tablespoon sugar and 1 8 teaspoon salt. Remove the baking sheet with the tart shell from the refrigerator. Arrange the apples in concentric circles so they overlap slightly. Brush the edges of the crust with the melted butter and then bake until the edges are golden and the apples have cooked down, about 1 hour. Cool for 15 minutes before slicing and serving.