Peel and finely chop the onion. Wash and dry the lime and grate the peel. Squeeze the lime juice. Wash the coriander, dab dry and chop finely, except for a few leaves for garnishing.
Mix lime juice and zest, diced onion and coriander. Gradually stir in olive oil. Season sauce with salt, pepper and sugar. Wash and clean the tomatoes, dab dry and cut into thin slices.
Cut the avocado in half, remove the core. Peel and slice the flesh. Drain mozzarella and cut into slices as well. Lay tomato, mozzarella and avocado slices alternately on top of each other, adding a little sauce between each layer.
Arrange tomato mozzarella towers with Parma ham on plates. Spread the rest of the sauce on the ham. Garnish with coriander leaves.