Roll and stretch the pizza dough into a 6-inch round.
Lay the dough round in the air fryer, then brush with 1 teaspoon of the olive oil.
Arrange the mushrooms over the dough, followed by the thyme leaves.
Sprinkle with the smoked mozzarella and chile flakes.
Season with salt and black pepper, drizzle with the remaining 1 teaspoon olive oil, and cook at 350°F until the dough is cooked through and the cheese is melted and golden brown, about 8 minutes.
