Thaw puff pastry at room temperature for 30-40 minutes or overnight in the refrigerator until pliable but still cool. Preheat oven to 400°F (200°C) and line a baking sheet with parchment paper.
Wash and dry peaches. Cut each in half along the seam, remove the pit, and slice 1/4 inch thick. You should have about 3 to 3.5 cups of sliced peaches.
In a large bowl, combine sliced peaches with 2 tablespoons sugar, cornstarch, lemon juice, vanilla extract, and cinnamon. Toss gently until evenly coated and let sit for 5 minutes.
Unfold the pastry onto the parchment-lined baking sheet. Gently roll into an 11-inch square or 12-inch circle about 1/8 inch thick, leaving a 1.5 to 2-inch border.
Spoon the peach filling into the center of the pastry, spreading in an even layer and leaving the border clear. Arrange top slices in a decorative pattern if desired.
Fold the outer 1.5 to 2-inch border up and over the peach filling, pressing gently to seal. Overlapping, uneven folds are perfectly fine and add rustic charm.
Whisk the beaten egg and brush a thin, even layer over the pastry border. Sprinkle with the remaining 1 tablespoon sugar or turbinado sugar for crunch.
Bake on the center rack at 400°F (200°C) for 22-28 minutes until the pastry is golden brown and the filling is bubbling and thickened. Rotate pan halfway through baking.
While the galette is hot, heat apricot jam with 1 tablespoon water until melted and smooth. Brush a thin layer of the glaze over the peach filling only for a glossy finish.
Let the galette rest on the baking sheet for at least 10 minutes before slicing. Serve warm with vanilla ice cream, whipped cream, or a drizzle of caramel sauce.