Mushroom and Kale Slab Pie

steps

1. Make the crust: In a food processor, pulse flour, butter, and salt until the butter is broken into small pieces and coated with flour. Add water and process until mixture almost forms a ball. Form dough into a 4×6-inch rectangle, using plastic wrap and a bench scraper to press dough into shape. Wrap tightly and refrigerate at least 4 hours.
2. Remove dough from refrigerator and allow it to warm slightly. Divide dough into two portions, one slightly larger than the other. Roll out larger piece to 11×15 inches and place in a quarter-sheet pan, pressing it into corners of pan and allowing excess to drape over sides; place in refrigerator to chill. Roll out second portion of dough to 10×14 inches; place it on a lightly floured sheet of parchment and refrigerate.
3. Make the filling: To a wide skillet over high heat, pour 1½ tablespoons olive oil and heat until shimmering. Add shiitake mushrooms and position into a single layer. Sprinkle with ⅛ teaspoon each salt and red pepper flakes. Leave the pan alone until a mushroom can be lifted easily without sticking, about 6 to 9 minutes. (Be brave: The mushrooms will smoke, snap, and sizzle.) Flip all mushrooms quickly and cook until the other side is equally browned, another few minutes. Transfer shiitakes to a bowl. Repeat with another 1½ tablespoons oil, cremini mushrooms, and ⅛ teaspoon each salt and red pepper flakes. Return shiitakes to pan. Add sherry and cook over high heat until scent of alcohol has diminished and most liquid has evaporated. Transfer mushrooms to a bowl and set aside.
4. To the pan, add remaining 1 tablespoon olive oil. Reduce heat to medium high and add onion and thyme, stirring to coat with oil. Reduce heat to medium and cook gently until onion is soft and golden brown, about 15 minutes. Stir in kale and remove from heat.
5. Preheat oven to 400 degrees; if you have one, place a baking steel, baking stone, or inverted baking sheet on the center rack to heat. Scatter mushrooms along bottom crust, add kale and onion, and gently push filling into the corners of crust.
6. In a medium bowl, whisk milk, 2 eggs, and egg white together with pepper and remaining ¾ teaspoon of the salt. Pour egg mixture over pie filling and distribute grated cheese across pie.
7. Drape top crust over filling, trimming edges to match edge of pan. Crimp top and bottom crust together; cut vents into top crust. Whisk reserved egg yolk with 1 teaspoon water in a small bowl. Use a pastry brush to paint top of crust with egg wash. Sprinkle with salt. Chill for 20 minutes, then bake on top of stone or baking sheet, if using, until a knife inserted into pie comes out clean, 45 to 50 minutes. Cool for at least 10 minutes before portioning. Refrigerate leftovers and bring them back to room temperature to serve, or wrap in foil and reheat at 350 degrees for 15 to 20 minutes.