Prepare the roasted garlic: Preheat the oven to 375degrees. Cut the top 1/2 inch off the heads of garlic. Place on a large piece of foil and drizzle with the olive oil. Wrap foil tightly and place the package in a small baking dish. Roast until soft and lightly browned, about 1 hour.
Meanwhile, prepare the tortilla cake: Combine the canola oil and onions in a large saute pan over medium heat. Cook for 5 minutes, stirring to caramelize but not over-brown. Add the butter and sugar. Once the onions have caramelized, remove from the heat and cool.
Once cooled, thoroughly mix the onions with the parmesan, mayonnaise and cilantro. Squeeze the roasted garlic out of their skins and stir into the onion mixture. Refrigerate for at least 30 minutes.
Set aside of the onion mixture for the dipping sauce. Spread 2 tablespoons of the mixture on top of a tortilla and cover with another tortilla. Repeat spreading and stacking the tortillas, finishing with a tortilla with no mixture on top. Wrap the tortilla stack in plastic wrap and let set up for 12 to 24 hours in the refrigerator.
After the stack has set up, cut into 16 wedges. Preheat a grill or grill pan; warm wedges over medium heat until both sides are marked. Combine the remaining onion mixture with the balsamic vinegar to make the dipping sauce.