Place the tomato, cucumber, red pepper, onion, garlic, basil, and mint in a large bowl. Drizzle with the oil and vinegar. Sprinkle with 1 tsp. salt. Let sit for 20 minutes or up to several hours refrigerated.
Puree to desired consistency in a blender or food processor. If needed, add ice water to thin the soup. Stir in hot sauce, if using. Taste and adjust seasoning.
While the soup is marinating, bring a small pot of salted water to a boil. Cook acini de pepe according to package directions. Drain and rinse under cold water. Stir into pureed soup.
Ladle soup into bowls and garnish with any leftover herbs.