Begin by pinching the stems off the beans (they won't soften in cooking). Then tear the tomatoes into large chunks (about 3 pieces each so it's easy to pick out their skins when they fall off later). Discard their eyes.
In a large saucepan or Dutch oven, warm 2 tablespoons of olive oil over high heat. Add the squashed garlic cloves and half of the basil. Cook until the garlic is sticky and the oil is fragrant, about 2-3 minutes. Then, add the tomatoes, beans, and a pinch of Kosher salt. Stir well, put the lid on, and cook, stirring occasionally, until the tomatoes have become a wet sauce and the beans are tender, about 15 minutes. Reduce the heat to low and continue to cook with the lid on until the beans are so soft they’re squashable, and some are beginning to split in half, about another 10 minutes.
Remove the lid and continue to cook, stirring more often, over low heat until the tomato sauce is tight and sweet, and beginning to stick to the bottom of the pan, about 15 minutes. Turn off the flame, taste for salt, add the remaining basil and olive oil, and pick out any bothersome tomato skins. Allow to cool slightly before eating.
EAT WITH a retro basil garnish, a grating of parm, tossed through pasta, spooned on top of rice or alongside grilled meat or fish; eat at room temperature with a tin of tuna and some hot sauce or olives. It keeps very well and - as is typical of braises - improves with sitting around.
