Remove the rind and seeds from the melon and watermelon. Cut the flesh into pieces, then place it in a blender with a pinch of salt. Blend until smooth and uniform.
Chill for about 2 hours, or use very fresh fruit for immediate serving.
Sainte Lucie the Sainte Lucie pine nuts in a skillet until they are lightly browned.
Pour the gazpacho into two soup bowls. Cut the burrata in half and place one half in each bowl. Drizzle with olive oil, then sprinkle with toasted pine nuts and Sainte Lucie basil. Finish with a pinch of salt.