Step 1

Make the crust: Pulse butter, flour, and 1 teaspoon salt in a food processor until it resembles coarse meal with some large pieces. Whisk together egg, yolk, and water. Pulse flour mixture, drizzling with egg mixture, until dough forms. Turn out dough onto plastic wrap; shape into a rectangle, and wrap. Refrigerate until firm, at least 1 hour.

Step 2

Roll out dough to a 14-by-21-inch rectangle on a lightly floured surface. Refrigerate until firm, about 15 minutes. Coat a rimmed baking sheet with cooking spray. Fit dough into sheet. Fold excess under, and pinch to form a crust that comes 1/2 inch above rim. Freeze until firm, about 30 minutes.

Step 3

Preheat oven to 375 degrees, with 1 rack in middle position and 1 rack in the lower third. Line dough with parchment, pressing flush and leaving a 2-inch overhang on all sides. Top with dried beans or pie weights. Fold parchment over crust edges. Bake on lower rack, rotating halfway through, for 40 minutes. Remove beans and parchment. Bake until golden brown and crisp, 15 to 17 minutes more. Let cool slightly on a wire rack.

Step 4

Reduce oven temperature to 325 degrees. Make the filling: Heat 2 tablespoons butter in a large skillet over high heat. Cook mushrooms until tender, about 8 minutes (adjust heat if needed). Season with 1/2 teaspoon salt and some pepper; transfer to a bowl.

Step 5

Let skillet cool. Add remaining tablespoon butter. Cook garlic over low heat, stirring often, until fragrant, about 1 minute. Stir in chard; season with 1/2 teaspoon salt and some pepper. Cook, covered, stirring occasionally, until tender, about 6 minutes. Raise heat to high. Cook until liquid evaporates. Toss chard with mushrooms. Let cool slightly.

Step 6

Whisk eggs with half-and-half and 2 teaspoons salt in a bowl. Sprinkle 1 1/4 cups cheese onto tart crust. Spread mushroom-chard mixture over top. Sprinkle with remaining 1 1/4 cups cheese. Slowly and evenly pour custard over cheese and vegetables. (It should come no higher than 1/4 inch from the top of crust; discard extra.) Bake on middle rack, rotating halfway through, until custard is just set, 35 to 45 minutes. Let stand on a wire rack for 15 minutes. Cut into squares. Serve immediately.