Put salted water on the stove. When it boils, add the pasta. Cook until al dente. Set aside 1 dl of the cooking water in a cup. Drain the pasta, but do not rinse with cold water. Set the cooked pasta aside.
Peel the onion and garlic. Cut the onion into large pieces.
Wash the basil leaves and dry them on a paper towel.
Pour oil into a high-sided frying pan or saucepan and add the whole garlic cloves and basil leaves. Fry slowly over medium heat until golden brown. Stir occasionally! Then pour everything, including the oil, into a heatproof bowl. It is very important to keep the oil, as it gives the sauce its spicy flavor.
Put the butter and onion in the same pan. Fry over low heat. Stir frequently to prevent burning. The butter will turn brown and the onion will caramelize. Delicious flavors! If you don't want the flavor to be too sweet, add a little salt to the onions at this point.
Add the chopped tomatoes and pour back in the reserved roasted garlic and basil leaves along with the oil. Pour the tomato juice left in the can into the reserved cooking liquid and add to the pot. Cook everything together for about 5 minutes.
Pour into a thermo glass blender or use a hand blender, the important thing is to blend until completely creamy. When ready, bring to the boil again in the saucepan.
Add the cooked pasta. Stir and serve while still warm.
When serving, sprinkle diced mozzarella cheese or grated Trappist cheese and fresh basil leaves on top.