To begin, heat the oven to 400°F. Then, cut the tomatoes in half and place them on a parchment lined baking sheet. Add the sliced onion, garlic cloves, oregano, salt and pepper.
Drizzle with olive oil, toss gently and arrange the tomatoes so the cut side is facing down. Then, put the sheet pan in the oven and roast for 30-40 minutes, until the tomato skins have loosened.
Allow the tomatoes to cool for about ten minutes and then, pull the skins off. They should come off very easily.
Then, put the roasted tomatoes, onions, and garlic into a food processor (leaving the liquid behind) along with the basil leaves and blitz. Taste and adjust seasoning as necessary.
Bring a pot of salted water to a boil and cook the spaghetti according to the package instructions. Drain the pasta and toss it with the sauce. Top with freshly torn basil leaves, and a sprinkling of Parmigiano-Reggiano.