Combine diced tomatoes, cucumber, bell pepper, green onion, jalapeno, and garlic in a large bowl. Stir in salt, cumin, oregano, cayenne pepper, and black pepper.
Place cherry tomatoes, olive oil, lime juice, balsamic vinegar, and Worcestershire sauce in a blender. Cover and puree until smooth. Pour pureed mixture through a strainer into the tomato-cucumber mixture; stir to combine.
Place 1/3 of the tomato mixture into the blender. Cover, turn blender on, and puree until smooth. Return pureed mixture to the remaining tomato-cucumber mixture. Stir to combine. Cover and chill in refrigerator for 2 hours.
Season cold soup with salt and black pepper to taste. Ladle into bowls and top with basil.