Place a large pot of water on the stove and bring to a boil.
Cook the spaghetti in the water and remove when it is just shy of al dente—depending on the pasta, 3 minutes for fresh, 10 minutes for dried.
Cut tomatoes in half lengthwise. Remove seeds with your thumb, and set seeded tomatoes aside. Reserve seeds and excess juices. If using canned tomatoes, seed in the same way.
Allow the tomatoes to cook for a few minutes until they begin to soften, then mash them with a potato masher or wooden spoon.
If the consistency is particularly thick, strain excess tomato juices for seeds and add to pot.
Allow tomatoes to cook 30 to 45 minutes over medium heat, smashing and stirring occasionally. Add tomato sauce in and stir.
While the tomatoes are cooking, prepare the basil-garlic oil.
Take a small saucepan and place 1/4 cup of extra virgin olive oil in the pan.
Add garlic cloves, basil, and chilli flakes.
Slowly heat to allow the flavors to transfer to the oil. When the garlic is lightly browned, remove from the heat. Allow to cool for 5 minutes.
Strain the oil through a chinois and combine with the tomato mixture.
Remove the sauce from the heat and adjust the seasoning with additional salt, as needed.
Allow the sauce to reduce slightly. Add the pasta to the sauté pan along with a bit of pasta water, to add starch and seasoning.
Add the pasta to the sauce, and allow to finish cooking, over medium high heat. The sauce should coat the pasta and look cohesive.
When you shake the pan, the sauce and pasta should move together.
Remove from the heat and add the basil, cheese, butter, and extra virgin olive oil. Toss until well incorporated.
Adjust the seasoning and serve immediately.