Mix crème fraîche and 1 tablespoon pesto and season to taste with salt and pepper. Cut the artichokes into slices. Cut the rolls in half and spread the halves with pesto cream. Cover the ciabatta halves with 2 slices of Parma ham each.
Spread the artichokes and the remaining pesto on top and sprinkle with coarse pepper. Garnish the ciabatta with basil.