Make the dough: In a bowl, whisk 1 1/4 cups flour, 1 tablespoon sugar, and 1/2 teaspoon salt. Cut in 1 stick cold butter (cubed) until pea-sized. Stir in 2–4 tablespoons ice water until it just comes together.
Press into a disk, wrap, and chill 30–60 minutes.
Prep the pears: Peel (optional), core, and slice pears 1/4-inch thick. Toss with 1/4 cup brown sugar, 1 tablespoon granulated sugar, 1 tablespoon cornstarch, 1/2 teaspoon cinnamon, 1/4 teaspoon ginger, a pinch of cardamom, zest of 1/2 lemon, 1 teaspoon lemon juice, and 1/2 teaspoon vanilla. Let stand 10 minutes.
Heat the oven: Set to 400°F (200°C).
Line a baking sheet with parchment.
Roll the dough: On a lightly floured surface, roll the chilled dough into a rough 12-inch circle. Transfer to the lined sheet.
Assemble: Arrange pear slices in the center, leaving a 2-inch border. Spoon any thickened juices over the fruit.
Fold the edges up and over, pleating as you go.
Finish the crust: Brush the edges with beaten egg and sprinkle with coarse sugar for crunch.
Bake: Bake 35–45 minutes, until the crust is deep golden and the filling bubbles. If the crust browns too fast, tent the edges with foil.
Optional glaze: Warm 1 tablespoon apricot jam or honey and brush over the pears for shine.
Cool slightly: Let sit 15 minutes so the juices set. Serve warm or at room temp, ideally with vanilla ice cream or whipped cream.