Heat the 1 Tbsp. oil in large skillet set over medium-high. Add the mushrooms and garlic and cook until the mushrooms are tender, about five to six minutes. Remove from the heat.
Preheat the oven to 425°F. Line two large baking sheets with parchment paper. Set two pitas on each baking sheet. Spread the top of each pita with tomato sauce. Top the sauce with the mushrooms, cheese, bell pepper and black pepper.
Bake the pita, one sheet at a time, 8 to 10 minutes, or until the toppings are hot and the bottom of the pitas are crispy. Cut and enjoy them, while you bake the other two pitas.
Top the baked pitas with the fresh basil and a drizzle of olive oil just before serving.