Salted Caramel-Apple Slab Pie

1. Make crust: Whisk together flour, granulated sugar, and salt in a large bowl. Cut in butter with two forks or a pastry blender until pieces are the size of small peas and mixture is crumbly. Drizzle in 1 1/2 cups ice-cold water, stirring just until dough starts to come together. Turn dough out onto a work surface and knead just until it comes together. Divide in half. Flatten each half into a rough rectangle (about 9 by 6 inches) and wrap with plastic wrap. Chill at least 2 hours or up to overnight. 

2. Make filling: Melt butter in a large skillet over medium-high heat. Add apples and cook, stirring often, until crisp-tender, 10 to 12 minutes. Stir in caramel sauce, brown sugar, salt, lemon juice, cinnamon, nutmeg, and cornstarch. Cook, stirring often, until mixture comes to a simmer and begins to thicken, 2 to 4 minutes. Remove from heat; stir in vanilla. Let cool.

3. Roll one piece of dough on a lightly floured work surface to a 19-by-14-inch rectangle; place in a 15-by-10-inch jelly-roll pan. Cover and chill 30 minutes.

4. Roll out second portion of dough on a lightly floured work surface to a 19-by-14-inch rectangle. Cut out 5 or 6 apple shapes with a 2-inch apple-shaped cutter, saving cut-outs and dough for top of pie. Cover and chill dough and cut-outs 30 minutes.

5. Preheat oven to 375°F with oven rack in bottom position. Whisk together egg and 1 tablespoon water in a bowl.

6. Spoon filling into crust in pan. Place top crust over filling. Trim any excess, fold edges under, and crimp. Place apple cut-outs on top of pie. Brush crust with beaten egg mixture. Sprinkle with coarse sugar. Bake until golden brown and filling is bubbly, 50 minutes to 1 hour. Cool on a wire rack 1 hour. Serve with vanilla ice cream and additional caramel sauce.