Using a 2" round cookie cutter or mouth of juice glass, cut circles in bread slices - try for two per slice - and arrange on baking sheet.
Slice onions ring-wise about 3/16" (4 mm) thick and lay one slice on each bread disc.
Mix equal parts mayonnaise and grated Parmesan, enough for about ½-1 tsp on each disc, and put glop on top of each onion slice.
Broil discs for 1-3 minutes or until golden brown on top. Serve hot.
Serves as many as you make!