Prepare all ingredients by cubing the chilled watermelon, peeling and dicing the cucumber into uniform 1/4-inch pieces, and measuring the lime juice and honey accurately.
Add the watermelon cubes to your high-speed blender or food processor and blend on high speed for 30-45 seconds until completely smooth and liquid.
Add the diced cucumber, fresh lime juice, basil leaves, honey, and sea salt to the watermelon puree. Blend on medium-high speed for 45-60 seconds until all ingredients are fully incorporated and the mixture is silky smooth.
Pour the gazpacho through a fine-mesh strainer into a large mixing bowl, pressing the solids gently with the back of a spoon to extract maximum liquid while removing any remaining pulp or herb pieces.
Taste and adjust seasoning by adding more lime juice for acidity, honey for sweetness, or salt for balance. Cover the bowl and refrigerate for at least 2 hours or until thoroughly chilled.
Serve in chilled bowls, garnished with fresh basil leaves, a drizzle of quality olive oil, and diced cucumber if desired. Stir gently before serving as natural separation may occur.