Grate onion using the coarse setting of a cheese grater. Add the grated onion and its juices into a pot. Add olive oil. Sweat onion over medium heat for 2-3 minutes.
Add tomatoes and crush to desired consistency with a potato masher. Salt to taste.
Heat sauce for just a few minutes over medium heat, until simmering. Stir often.
Remove pot from heat. Add butter and swirl in until melted. Add a handful of cheese and basil. Stir again. Serve!
Video
Notes
Use the homemade sauce on: pasta, lasagna, pizza, calzones, chicken parmesan, veggie noodles, stuffed peppers, meatballs, etc.!
You can add a handful of fresh basil to your sauce when you swirl in the butter, if desired! See the above post for more variations and additions.