Before you start be sure you have two empty bowls and a fine-mesh strainer ready to use.
TO PEEL THE TOMATOES:
Bring a large pot of water to boil. Once the water comes to a boil, reduce the heat to medium low.
Prepare a similar-sized bowl of ice water.
Make a shallow X in the bottom of each tomato using a sharp knife. All at once, place the scored tomatoes into the pot of simmering water. After 30 seconds, remove the tomatoes using a slotted spoon and place in the ice water bath.
When cool, peel each tomato, starting at the X, and discard the skins.
TO MAKE THE SAUCE:
Quarter each peeled tomato straight down from the top to create four “petals,” then place the quarters in the bowl of a food processor. Pulse initially 3 or 4 times to break up large pieces, then process until the sauce has a texture similar to salsa. Don’t make it totally smooth.
Place a fine-mesh strainer over a bowl and pour the tomato purée into it. Allow to strain for about 30 seconds to remove the very watery juice, then pour the purée into a clean bowl, adding the olive oil, salt, basil, pepper and garlic. Stir until the ingredients are well incorporated.
Cover and allow the flavors to marinate for at least an hour, or store in the refrigerator overnight.