- twelve 7- to 8-inch flour tortillas
- 1 1/2 pounds red onions, chopped fine (about 3 cups)
- 2 tablespoons olive oil
- 3/4 cup minced fresh parsley leaves
- 1/3 cup freshly grated Parmesan cheese
- 3/4 cup mayonnaise
- 1 tablespoon balsamic vinegar
- about 3 dozen wooden picks
- Prepare grill
- On a rack set about 5 inches over glowing coals toast tortillas lightly a few at a time, turning them once, until they begin to puff on each side but are still soft. Alternatively, tortillas may be toasted on a stove-top griddle over moderately high heat.
- In a large non-stick skillet cook onions in oil over moderately low heat, stirring occasionally, until soft, about 15 minutes. Transfer onions to a bowl and cool. Stir in parsley, Parmesan, 1/2 cup mayonnaise, and salt and pepper to taste.
- Spread onion mixture on 11 tortillas, stacking them, and top the stack with remaining tortilla. Wrap cake well in plastic wrap and chill at least 1 hour and up to 4 hours.
- Discard plastic wrap and with large sharp knife cut cake into 3/4-inch-wide slices (not wedges). Turn each slice onto its side and secure ends and middle with wooden picks.
- In a small bowl stir together vinegar and remaining 1/4 cup mayonnaise and brush some of mixture on a cut side of each slice.
- Grill slices, mayonnaise sides down, until golden brown, 3 to 4 minutes. Brush tops with remaining mayonnaise mixture, turn slices, and grill until golden brown, 3 to 4 minutes more.
- Alternatively, broil slices on rack of broiler pan about 4 inches from heat, mayonnaise sides up, until golden brown, 3 to 4 minutes. Turn slices and brush tops with remaining mayonnaise. Broil until golden brown, 3 to 4 minutes more.
- Discard wooden picks