Fill a 6-quart pot halfway full of water, set over high heat, and bring to a boil.
Meanwhile, make an "X" with a paring knife on the bottom of each tomato. Drop the tomatoes in the boiling water for 15 seconds, remove, and transfer to an ice bath until cool enough to handle, about 1 minute. Remove and pat dry. Peel and halve the tomatoes. Seed the tomatoes, putting the seeds and pulp in a fine mesh strainer set over a bowl in order to catch the juice. Press as much of the juice through as possible and then add enough bottled tomato juice to bring the total to 1 cup. Chop the tomato flesh.
Combine the tomatoes and juice in a large mixing bowl. Add the cucumber, bell pepper, red onion, jalapeño, garlic, olive oil, lime juice, balsamic vinegar, Worcestershire, salt, cumin, and pepper and stir to combine.
Transfer 1 1/2 cups of the mixture to a blender and puree for 15 to 20 seconds on high speed. Return the pureed mixture to the bowl and stir to combine. Cover and chill for at least 2 hours or up to overnight. Serve with thinly sliced basil.