Preheat oven and prepare flatbread: Preheat oven to 400°F. Unroll the pizza dough and press it into a 12-inch rectangle on a large baking sheet lined with parchment paper. Brush the dough with 1 tablespoon of the olive oil and sprinkle with garlic powder, oregano and salt.
Sauté the mushrooms: In a large skillet, melt the butter with the remaining 1 tablespoon olive oil over medium-high heat. Add the sliced mushrooms and cook, stirring occasionally, until they release their moisture and begin to brown, about 5-7 minutes. Add the minced garlic and thyme and cook for 1 minute more, until fragrant. Season with salt and pepper.
Bake the flatbread: Bake the prepared flatbread for 10 minutes. Remove from oven and top evenly with the sautéed mushrooms. Sprinkle the mozzarella and Parmesan cheeses over the top.
Finish baking: Return the flatbread to the oven and bake for an additional 5-7 minutes, until the cheese is melted and the crust is golden brown.
Serve: Remove the flatbread from the oven and sprinkle with the chopped fresh parsley. Slice and serve immediately.