Heat a medium saucepan over medium heat and add 2 tablespoons of olive oil. Once the oil is hot, add the chopped onion and cook, stirring often, until soft and golden (about 5 minutes).
Add the diced shallots and cook for about 2 more minutes.
Add the minced garlic and cook for 1 minute, or until fragrant.
Stir in the diced tomatoes, fire-roasted tomatoes, salt, and pepper to taste. Bring to a light boil, then reduce the heat and simmer partially covered for 15 minutes.
If you added cheese, remove the brine and cut the melted cheese off. Place the cheese back in the pot.
Use an immersion blender to create a smooth sauce.
Pour in 1 cup of vegetable stock and stir on medium heat for three minutes.
Finally, stir in the chopped fresh basil, then turn off the heat.
Serve the sauce with your favorite pasta and top with shaved Parmesan Reggiano and fresh basil.