Rinse, pat dry and chop oysters. Combine in a bowl with bread crumbs, onions, garlic, parsley, Parmesan, eggs. Form into cakes about 3 inches high and 1 inch wide. Chill, uncovered, about 30 minutes.
Meanwhile, prepare mayonnaise. In a small bowl combine mayonnaise, cream, capers, and pepper and blend well. Refrigerate.
Heat about cooking oil to a depth of 1/4 inch in heavy skillet over medium high heat. Add cakes, being careful not to crowd them in the skillet. Brown on both sides, about 3 minutes a side.
Serve on bed of shredded lettuce with caper-cayenne mayonnaise.
