Cut the peppers into large pieces, removing the cores and seeds. Lay skin-side up under a preheated grill and cook until the skin blackens and blisters. Transfer to a plastic bag, tie the top to enclose and leave to cool, then peel away the skin.
Place the peppers and garlic in a food processor and blend until fairly smooth. Stir in the spring onions and set aside.
Cook the tortellini in a large saucepan of boiling water according to the packet instructions until al dente. Drain and return to the pan.
Toss the pepper mixture into the pasta and add the oil and Parmesan. Season to taste with salt and pepper and serve immediately.