► FILLING: Preheat oven to 375°F. In a medium bowl, toss tomatoes with olive oil and salt. Place on a parchment-lined baking sheet and roast until lightly caramelized, about 15 minutes. Remove from oven and set aside.
►In a large skillet, heat neutral oil over medium heat until slick and shiny. Add mushrooms, soy sauce, and fish sauce and sauté, stirring only occasionally, until mushrooms are lightly crispy and browned, about 8-10 minutes. Season with salt and black pepper; remove from heat and set aside.
►GALETTE: Raise oven temperature to 400°F. Carefully roll out pie crust, and place mushrooms in center. Smooth out mixture in flat layer, then top with tomatoes, leaving roughly ½-inch room at edges. Fold edges of pastry into middle 6 to 8 times, leaving filling exposed in the center.
►Bake galette on the middle rack of the oven until crust is golden brown, 25 to 30 minutes. Remove from oven and cool. Top galette with parsley and lime juice before serving.