PREPARE A POT OF BOILING WATER and an ice bath. Core the tomatoes, cut a small x on the bottom, then blanch the tomatoes in the boiling water for 1 minute and, using a slotted spoon or a spider, transfer them to the ice bath. When cool enough to handle, remove the skins with a paring knife and discard them. Slice the tomatoes in half and strain through a fine-mesh sieve set over a bowl. Discard the seeds but reserve the liquid. Combine the deseeded, peeled tomatoes, reserved juice, and salt in a large bowl. Mix the salt into the tomatoes and set aside.
Place the garlic in a saucepan, cover with the olive oil, and cook over very low heat until the garlic is golden and soft, about 20 minutes. (Watch it carefully and shake the pan occasionally to make sure the garlic doesn’t burn.) Strain and reserve the garlic-infused oil).
In a large heavy-bottomed stockpot, cook the red pepper flakes in the infused garlic oil over low heat for about 2 minutes, until the red pepper flakes become fragrant, and the flavor starts to bloom. Add the salted tomatoes and tomato liquid to the pot and raise the heat to medium-high. Bring the liquid to a slight boil and skim off the foam that rises to the top. Reduce the heat to medium low, and then, using a potato masher, mash the tomatoes very finely as they cook.
Simmer until the sauce is reduced by one-fourth, about 25 to 30 minutes, then taste and adjust the seasoning with salt.
Remove from heat and stir in the basil. Prepare with handmade pasta or store bought pasta according to the directions. (The sauce can be kept in the refrigerator in an airtight container for up to a week, or in the freezer for about 1 month. Cool the sauce to room temperature before storing it.)