In a 12-inch skillet over medium-high, combine 3 tablespoons oil and the garlic. Cook, stirring, until the garlic is golden brown, 2 to 3 minutes. Remove and discard the cloves or reserve for another use. Add the tomato juices to the pan. Bring to a simmer and cook, stirring often, until thick enough that a spatula drawn through the mixture leaves a trail, 4 to 5 minutes.
Add the mashed tomatoes and cook, stirring often, until slightly thickened, about 5 minutes. Off heat, stir in the remaining 1 tablespoon oil. Taste and season with salt, then stir in basil (if using).
