In a 10-inch-diameter nonstick sauté pan, heat the oil over a medium flame. Add the pasta mixture to the pan, spreading evenly. Cook until golden brown on the bottom, about 8 minutes. Carefully invert the pasta mixture onto a plate, then slide it back into the pan. Continue cooking until the bottom is golden brown and the mixture is heated through, about 6 minutes. Transfer the pasta mixture to a serving platter and sprinkle with Parmesan cheese. Cut into wedges and serve warm.