1. Place all ingredients in a blender and purée. Set aside.
2. Preheat oven to 350°F. Place flatbreads on 2 large cookie sheets sprayed with nonstick cooking spray. Bake 5 to 7 min. Remove from oven and top each flatbread with 1/4 of the romesco sauce.
3. Reset oven to 375°F. In a bowl, toss Mozzarella and Smoked Gouda together. Sprinkle the cheese, divided equally, over the 4 flatbreads. Top each with mushroom slices and sprinkle with red pepper flakes. Bake until cheese melts and crusts crisp, about 12 min. Sprinkle pizzas with fresh basil, if desired.