Peel the zucchini with the peeler (put the pesto peel aside) and arrange the resulting wide ribbons on two plates.
Cut the part that is not suitable for the ribbons into cubes and place in a bowl with the finely chopped zest of the zucchini. Cut the garlic clove very finely and mash it with the salt.
Halve the avocado, remove the stone, remove the pulp with a teaspoon and add to the bowl along with the garlic, juice and pulp of a lemon, finely chopped basil leaves and spices to taste.
Add a little water (carefully, it is better to pour in again) and mix with a hand blender to a mass. Now pour this pesto over the zucchini ribbons and sprinkle a little nutmeg on top if you like.