Place 4 tomatoes in a blender, and then add 4 radishes, 1 cucumber, 1 bell pepper, the fennel, scallions, parsley, and lemon juice. Puree until very smooth, about 1 minute.
Line a large bowl with 3 layers of cheesecloth. Pour puree into the bowl, gather cheesecloth around puree, and tie into a bundle. Tie ends to a long wooden spoon, and balance spoon on the rim of a deep pot, suspending bundle in the pot. Refrigerate and strain for 2 hours to extract a clear broth.
Gently squeeze solids in cheesecloth to extract liquid. (You should have 4 cups liquid.) Discard solids.
Season broth with salt and cayenne pepper. Garnish with remaining tomato, radish, cucumber, bell pepper, and parsley. Drizzle with oil and vinegar, and serve cold.
The broth from this soup can be served as a cold beverage instead of soup.