Prepare vegetables: Core tomatoes and cut into 1-inch chunks. Reserve ¼ cup tomato seeds in small bowl for garnish. Add half tomato chunks to blender, half to serving bowl. Add all onion chunks to blender.
Divide remaining vegetables: Cut off one-fourth of cucumber, finely chop and place in garnish bowl. Slice rest into 1-inch chunks, divide between blender and serving bowl. Repeat with bell pepper, reserving finely chopped portion for garnish.
Blend base: Add basil, garlic, olive oil, vinegar, salt, and 10 twists black pepper to blender. Secure lid and blend on low, increasing to high, until completely smooth (about 2 minutes).
Add texture: Pour reserved chunks from serving bowl into blender. Pulse 10-20 seconds until broken into small pieces. Stop here for texture, or blend longer for smaller pieces.
Season and chill: Add pinch of salt to garnish bowl, stir, and refrigerate. Chill soup at least 2 hours or up to 24 hours for flavors to develop.
Serve: Taste and adjust salt or pepper if needed. Divide into bowls, top with reserved garnishes, fresh basil, and black pepper. Serve cold.