In a medium bowl, mix the flour, kosher salt, and baking powder. Slice the butter into small pieces, then use a pastry blender or fork to cut it into the flour mixture until mostly incorporated and a pebbly texture forms (with pea-sized or smaller pieces).
Sprinkle 4 tablespoons of the cool water over the flour, mixing gradually with a fork until the flour is mostly incorporated. Add the additional 1 to 2 tablespoons of water until all the flour is incorporated, kneading with your fingers until the dough comes together. (Resist the urge to add more water; it should come together!) Form the dough into a ball and flatten into a thick disk. Wrap it in plastic or place it in a covered container and chill the dough for 1 hour. (To make in advance, you can refrigerate the dough up to 3 days; allow to sit at room temperature 30 minutes before rolling. Or, wrap in plastic wrap or aluminum foil and freeze up to 3 months, then defrost overnight in the refrigerator before rolling.)
Preheat the oven to 400 degrees Fahrenheit.
Clean and slice the mushrooms. Toss them in a bowl with the olive oil, soy sauce, garlic powder, onion powder, smoked paprika, thyme, and 1/2 teaspoon kosher salt. Place them in a single layer on a parchment lined baking sheet and bake for 20 minutes until tender.
In a medium bowl, mix the ricotta cheese, Parmesan cheese, garlic, 1/4 teaspoon kosher salt, and a few grinds black pepper.
On a floured surface, roll the dough into an even 12” circle, leaving the edges rough (if needed, move the dough around and add a bit more flour underneath to keep it from sticking). Carefully transfer the dough to a sheet of parchment paper on a rimmed baking sheet.
Gently spread the ricotta mixture on the dough, then add the mushrooms, leaving at least 2 inches of dough around the outside edge. Fold in the outside edges of the dough over the filling to form an approximately 2-inch crust, overlapping the folds as shown in the photos. Top with fresh thyme leaves.
Whisk the egg and use a pastry brush to brush it onto the crust. Then top the crust with a small sprinkle of flaky sea salt.
Bake the galette for 30 to 33 minutes until the crust is golden brown. Remove from the oven and transfer the parchment paper to a baking rack to cool. Cool for at least 10 minutes, then slice into pieces and serve. It’s also great at room temperature or cold. Store leftovers for up to 3 days refrigerated; bring to room temperature or warm in the oven before serving.