At least 15 minutes before you want to serve your soup, warm a soup plate in the oven (at about 1ooC/200F) and put the broth on the simmer.
In a skillet large enough to hold your slices in one layer, melt a good nob of butter and fry the bread slices in the butter until golden brown on each side.
Remove the hot dishes from the oven and place the bread slices flat on the bottom of each plate. Crack an egg over each slice. Top with a generous sprinkling of freshly grated Parmesan cheese.
Raise the heat and bring the broth just to the boil, then pour the hot broth into the soup plate, making sure that you don't move the egg off the bread. It is best to add the broth at the sides, not directly over the eggs. The heat of the broth should cook the eggs slightly.
Serve immediately—and warn your guests that the plates are hot!