Prepare the roasted garlic: Preheat the oven to 375 degrees. Cut the top 1/2 inch off the garlic heads and discard. Place the heads on a large piece of foil and drizzle with the olive oil. Wrap up foil tightly; place the package in a small baking dish. Roast until the garlic is soft and lightly browned, 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 (don't over brown). Add the butter and sugar; cook, stirring to caramelize. Remove from the heat and let cool.
Once cooled, mix the onions with the parmesan, mayonnaise and cilantro in a bowl. Squeeze the roasted garlic out of their skins and stir into the onion mixture. Refrigerate for at least 30 minutes.
Set aside 1/3 of the onion mixture in the refrigerator for the dipping sauce. Spread 2 tablespoons of the remaining mixture on top of a tortilla and cover with another tortilla. Repeat, spreading and stacking the tortillas; finish 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 reserved onion mixture with the balsamic vinegar to make the dipping sauce.
Photograph by James Baigrie
Recipe courtesy Guy Fieri for Food Network Magazine