Preheat the oven to 400°F and position an oven rack in the lower third. On a parchment paper, roll the pastry dough into a 13-inch circle and lift the parchment paper with the dough onto a baking sheet. Chill for 1 hour.

Heat the 1½ tablespoons olive oil in the medium sauté pan over medium-high heat. Add the onion and cook, stirring occasionally, until soft and lightly colored, 8 to 10 minutes. Stir in the thyme, ¼ teaspoon salt, and 5 grinds pepper and blend well. Transfer to a plate and set aside to cool.

Combine the cooled onion mixture, cheese, and potatoes in the large bowl. Mound the filling in the center of the chilled tart shell, leaving a 1½-inch border at the edge. Fold that border up around the filling, pleating it to make a pretty, circular enclosure and leaving the center open. Drizzle the filling with the remaining 1 tablespoon olive oil and sprinkle lightly with salt and 3 grinds of pepper. Lightly brush the pleated dough with the beaten egg to give it shine and help it brown in the oven.

Bake the galette for 45 to 50 minutes, until the pastry is golden brown and the potatoes are soft when tested with a paring knife or skewer. Use the metal spatula to lift the edge of the galette slightly and check underneath. The bottom crust should be a beautiful brown color. Transfer to a rack to cool for 5 to 10 minutes.

Carefully transfer the galette to a serving plate with the cake lifter, 2 spatulas, or a tart pan bottom supporting the bottom as you move it. Slice with a chef’s knife and serve warm. If you like, serve with dollops of crème fraîche or sour cream. Store uncovered at room temperature for up to 6 hours. Or cover with plastic wrap and refrigerate for up to 2 days. Reheat in a 400°F oven for 10 to 15 minutes before serving.