Halve the avocados, remove the stone and then the flesh from the skin. Puree the flesh with the lemon juice, season with salt and pepper. Mix the aceto balsamico with the oil, salt and pepper. Cut the radicchio in strips and combine with the dressing. Cut the cheese in thin slices.
Spread each slice of toast with some mustard. Cover each slice with avocado puree, Italian chicory and Emmentaler Switzerland AOP. Cover each piece of toast with one of the remaining slices and apply gentle pressure. Using a sharp knife, cut each toast sandwich diagonally to form two triangle shapes.