Preheat the oven to 425°F (220°C).
Roll the puff pastry dough out into a 12-14 inch (30-35 cm) circle on a lightly floured surface. It can be a rustic circle, no need for perfection. Place the dough onto a sheet of parchment paper or in a greased 12-inch cast iron skillet.
In a large bowl, combine the cherries, cornstarch, sugar, lemon juice, vanilla, almond extract, and salt and toss it all together to coat. 450 g dark sweet cherries, 65 g granulated sugar, 15 g cornstarch, 2 tsp lemon juice, 1 tsp vanilla extract, 1/4 tsp almond extract, 1/4 tsp salt
Pile the cherry mixture into the center of the dough, leaving a 2-3 inch (5-7 cm) border. Fold the edges of the dough over the filling, overlapping the folds as you work your way around the circle.
If you're not baking it in a skillet, transfer the galette on the parchment paper to a baking sheet.
In a small bowl, whisk the egg and water together. Brush the pastry edges with the egg wash and sprinkle generously with turbinado sugar. 1 large egg, 1 Tbsp water, Turbinado sugar for sprinkling
If your oven isn't at temperature yet, place the unbaked galette in the fridge while you wait.
Bake at 425°F (220°C) for 15 minutes, then turn the oven down to 375°F (190°C) and continue baking for around 40 minutes more, until the edges are a deep golden brown and the cherry filling is bubbly and thick.
Let the galette cool for at least 20 minutes before serving so the juices can set. Serve with vanilla ice cream or whipped cream.