Make the dough. In a bowl, whisk the flour, sugar, and salt.
Cut in the cold butter with a pastry cutter or your fingertips until you have pea-sized bits. Drizzle in ice water, 1 tablespoon at a time, tossing just until the dough holds together when pressed.
Chill. Form the dough into a disc, wrap it, and chill for 45–60 minutes. Cold dough means a flaky crust.
Prep the fruit. In a large bowl, combine pears, cranberries, granulated sugar, brown sugar, cornstarch, cinnamon, ginger, cardamom, vanilla, lemon juice, and a pinch of salt.
Toss gently to coat. Let it sit for 10 minutes to start releasing juices.
Heat the oven. Preheat to 400°F (200°C). Line a baking sheet with parchment paper.
Roll the dough. On a lightly floured surface, roll the chilled dough into a 12-inch round.
Transfer to the parchment-lined sheet.
Assemble. Pile the fruit in the center, leaving a 2-inch border. Spoon any light juices over the fruit, but hold back any large puddles to avoid sogginess.
Fold and seal. Fold the edges of the dough up and over the fruit, pleating as you go. Press gently to seal.
Brush the crust with beaten egg and sprinkle with coarse sugar.
Bake. Bake for 35–45 minutes, until the crust is deeply golden and the filling is bubbling. If the edges brown too fast, tent loosely with foil.
Finish and cool. If you like a glossy look, brush the fruit with warmed apricot jam or honey. Let the galette cool for at least 20–30 minutes so the juices thicken.
Serve. Slice and serve warm or at room temperature.
Ice cream, whipped cream, or a spoonful of crème fraîche is a great match.