In a large pot, heat the olive oil over medium heat. Add the diced onion and sauté for about 5 minutes, or until they become translucent. Add the minced garlic and cook for another minute, stirring frequently to avoid burning.
Pour in the crushed tomatoes and vegetable broth. Stir in the oregano, sugar, and red pepper flakes (if using). Bring the mixture to a simmer and let it cook for 10 minutes so the flavors can meld.
Add the cheese tortellini to the pot and cook according to the package instructions, usually about 3-5 minutes, until they float to the top and are tender.
Once the tortellini is cooked, reduce the heat to low. Pour in the heavy cream and add the chopped basil. Stir gently and let the soup heat through for another 2-3 minutes. Season with salt and pepper to taste.
Ladle the soup into bowls and top each serving with grated Parmesan cheese and a few extra basil leaves for presentation. Serve hot with crusty bread on the side if desired.