While the spaghetti is cooking, in a large skillet or pot add the extra virgin olive oil and bring to high heat. Next, add the garlic and onion and sauté for 4 minutes, mixing occasionally.
Next, add the roasted red peppers, olives, salt, and ground black pepper. Sauté for 5 minutes, mixing occasionally.
Next, add the pasta water, cheese, and basil and cook for 4 minutes, mixing occasionally.
Finally, add in the cooked pasta and cook for 2 minutes, mixing occasionally to incorporate all of the ingredients.