Puree half of the basil and mint together with the olive oil in a blender and set aside.
Halve the avocado, remove the pit, scoop out the flesh and cut into cubes. Peel the cucumber and chop with the garlic and onions.
Finely puree the avocado cubes together with the vegetables, the remaining herbs, some water and a dash of lime juice. Add salt and pepper to taste.
Chill the avocado gazpacho for 1-2 hours. After that, stir it again thoroughly.
Divide among glasses or bowls, garnish with the basil-mint oil and serve.