Purée tomatoes in batches in a blender, adding 1 tsp. salt, 1/4 cup oil, and the vinegar to final batch.
Strain purée through a fine-mesh strainer into a large bowl or pitcher. Season to taste with salt if you like. Serve chilled or at room temperature, garnished with a drizzle of oil and a sprinkle of basil.
Make ahead: Up to 2 days, chilled.
Note: Nutritional analysis is per serving.