Preheat the oven to 375 degrees F.
Line a baking sheet with baking parchment and set it aside.
In a bowl, combine the cherries with 1/3 cup of brown sugar, flour, lemon juice, lemon zest, almond extract, and salt. Using a potato masher, mash the mixture a few times to help release the juices of the cherries. Set it aside to allow the flavors to meld.
Place the chilled pie dough on the prepared baking sheet.
Add the cherry filling onto the center of the dough, leaving a 2-inch border around the edges. Spread it out evenly for uniform cooking.
Fold the edge of the dough up and over the cherry filling, overlapping and creating pleats around the edge. This rustic look adds charm to your galette.
In a small bowl, beat the egg with the water to create an egg wash. Brush the dough with this mixture to give it a beautiful golden finish.
Sprinkle the top of the galette and the crust edge with 1 tablespoon of brown sugar and 1 tablespoon of white sugar. This will add a lovely sweetness to the crust.
Bake in the preheated oven for about 40 to 50 minutes, or until the crust is golden brown and cooked through. Keep an eye on it towards the end of the baking time.
Transfer the galette to a wire rack to cool for a few minutes before slicing. Serve warm or at room temperature, preferably with a scoop of vanilla ice cream.
