3 tablespoons olive oil
2 garlic cloves, grated on a microplane
1½ teaspoons kosher salt, plus more to taste
½ teaspoon freshly ground black pepper
2 basil sprigs—leaves picked and lightly torn, sprigs reserved
Using the coarse side of a box grater, grate the cut sides of the tomatoes into a medium bowl until you reach the skin. Discard the skins. Strain the tomatoes through a fine-mesh strainer, gently pushing on the pulp to extract most of the juice. Reserve the juice for another use and transfer the tomato pulp to a quart-size mason jar. Add the olive oil, garlic, salt, pepper and basil sprigs. Seal with the lid and shake. Let sit at room temperature for 30 minutes to infuse. Discard the basil sprigs before using and add fresh basil to serve.