Boil the asparagus in salted water with sugar for about 14 minutes, drain and let cool.
Mix the basil with the olive oil, vinegar, sugar, salt and pepper. Halve thick asparagus spears.
Arrange the asparagus, mozzarella and avocado on a plate. Spread the tomatoes on top and pour the vinaigrette over it and sprinkle some basil leaves on top.