1. In a food processor or with a knife, mince cucumber, onion, tomato, and jalapeño.
2. Scrape vegetable mixture into a large bowl, stir in buttermilk, and season to taste with salt and pepper.
3. Serve soup with a few ice cubes added to each bowl. Or nest mixing bowl in ice and stir often until cold, about 10 minutes, then ladle into bowls.