Step 1In a wide, heavy skillet, heat the olive oil over medium heat. Add the garlic and cook, stirring, until fragrant, about 30 seconds. Stir in the tomatoes, basil, sugar and salt and increase the heat to medium-high. When the tomatoes are bubbling briskly, stir and reduce the heat to a gentle simmer.
Step 2Cook, stirring from time to time and scraping the sides and bottom of the pan, until the tomatoes have separated from their skins and cooked down to a thick sauce. Timing will depend on the type and ripeness of the tomatoes, anywhere from 30 minutes to an hour.
Step 3Remove the basil sprigs from the sauce and gently scrape off the sauce that clings to them.
Step 4Place the mixture in a food mill fitted with the fine blade, and press the tomato sauce into a bowl. Taste and adjust the seasoning as desired. Use at once, refrigerate for up to 4 days, or freeze in small containers or freezer bags.