Make the salsa verde by putting all the ingredients in a small food processor or blender and processing in long pulses until fully combined but not completely smooth.
In a large skillet, heat the olive oil over medium heat. Add the sliced green onions and cook until softened and translucent, about 5 minutes. Add the minced garlic and cook for an additional minute until fragrant. Add the sliced mushrooms to the skillet and cook until they release their moisture and become golden brown, about 8-10 minutes. Stir in 2 tablespoons Marukan Lite Seasoned Rice Vinegar and cook for another 2-3 minutes. Season with salt, pepper, and fresh thyme leaves. Remove from heat and let the filling cool slightly.
In a small bowl, combine the ricotta cheese and 1 tablespoon Marukan Lite Seasoned Rice Vinegar. Mix well until smooth.
Preheat your oven to 375°F (190°C) and line a baking sheet with parchment paper.
Roll out the pie crust on a lightly floured surface into a rough circle about 12 inches in diameter. Transfer the rolled-out dough to the prepared baking sheet.
Spread the ricotta mixture evenly over the center of the dough, leaving about a 2-inch border around the edges. Spoon the mushroom filling over the ricotta mixture. Sprinkle grated Parmesan cheese over the mushroom filling.
Fold the edges of the dough up and over the filling, pleating as needed to create a rustic galette shape. Brush the edges of the dough with beaten egg to help them brown in the oven. Bake for 30-35 minutes, or until the crust is golden brown and crispy.
Slice the mushroom and ricotta galette into wedges and serve warm with the salsa verde.