Caramelized Onion with eggs

4 teaspoons olive oil 2 cups onions , chopped 6 large eggs , hard boiled 2 teaspoons mayonnaise 2 teaspoons Dijon mustard 1 tablespoon oil-cured black olive ,[...]

1 tablespoon butter or 1 tablespoon margarine 4 cups sliced sweet onions (such as Vidalia) 1 tablespoon light brown sugar 3 cups cooked rice 2/3 cup freshly[...]