Combine. Add the flour, sugar, and salt to a food processor and pulse a few times to combine.

Cut in the butter. Add the cold cubed butter and pulse about 15 seconds, until the mixture looks like coarse breadcrumbs with pea-sized pieces of butter still visible.

Add the water. Add the ice water 1 tablespoon at a time, pulsing after each, until the dough looks crumbly but holds together when you squeeze a handful. You may not need all 12 tablespoons.

Shape and chill. Turn the dough out, divide it in half, and press each half into a flat rectangle about 1 inch thick. Wrap and refrigerate at least 30 minutes, or up to 2 days.

Prep the apples. Peel, core, and thinly slice the apples, about ¼ inch thick. Halve any large slices so they lay flat in the pan.

Bloom the spices. In a large pot or Dutch oven over medium heat, melt the butter with the brown sugar, cinnamon, and nutmeg. Let it bubble gently for about 2 minutes, stirring, until fragrant.

Thicken. Sprinkle the flour over the butter mixture and stir for about 1 minute, until it forms a smooth paste.

Cook the apples. Add the apples and lemon juice and toss until every slice is coated. Cook about 10 minutes, stirring occasionally, until the apples are slightly softened and the juices are thick and glossy. Take the pot off the heat and let the filling cool slightly while you roll the dough.

Preheat the oven to 400°F.

Roll the bottom crust. Let one rectangle sit on the counter for 5 minutes. On a lightly floured surface, roll it to about 12 x 17 inches (2 inches bigger than a 10 x 15-inch jelly roll pan on every side). Roll it loosely around your rolling pin, unroll it over the pan, and gently press it into the corners and up the sides, letting the excess hang over the edges.

Fill. Spread the apple filling and all of its buttery juices evenly over the crust.

Cut the strips. Roll the second rectangle to 12 x 17 inches and cut it into 1-inch strips with a knife, pizza cutter, or ravioli cutter for fun wavy edges.

Weave the lattice. Lay half of the strips lengthwise across the filling, about 1 inch apart. Fold back every other strip, lay one strip across the short way, then unfold the strips over it. Repeat, alternating which strips you fold back, until the top is covered.

Egg wash. Whisk the egg with 1 tbsp water, brush it over the lattice and edges, and sprinkle with the coarse sugar.

Bake. Bake at 400°F for 15 minutes, then lower the oven to 350°F and bake about 45 minutes more, until the crust is deep golden and the filling is bubbling through the lattice. Tent with foil if the edges brown too fast.

Cool at least 1 hour so the filling sets, then cut into squares.

Serve with vanilla ice cream and homemade salted caramel.