Set aside the reserved half of the chopped cucumber, tomatoes, red pepper and green onions and place the remaining half in a blender. Add the watermelon, garlic, basil, vinegar, olive oil, salt, pepper and jalapeño pepper, if using. Blend until smooth. Taste and adjust seasonings.
Pour into a large bowl (or small individual jars, as pictured) and stir in the reserved chopped vegetables.
Chill for 3 to 4 hours or overnight. Serve with drizzled olive oil.
Optional: garnish with diced avocado and/or micro greens before serving.