For the aioli: Place the mustard, egg yolks and garlic in the bowl of a food processor, and blend until smooth. Slowly add in the canola oil in a thin stream, thinning out with the lemon juice as needed. Season with salt and pepper and transfer to a mixing bowl. Mix in the hearts of palm.
For the relish: Heat a large, heavy-bottomed cast-iron pan. Place the kalamata and manzanilla olives in the skillet and cook to char, being careful not to shake or move the olives around. Transfer to a cutting board and finely chop the olives, capers, garlic and shallots. Mix with the olive oil and set aside.
For the steak: Preheat the grill or a grill pan. Sprinkle the steak with olive oil, salt and pepper, and grill.
Stack two slices of the rib eye with one slice of ham, one slice of mortadella and top with a slice of provolone. Repeat for the remaining meat and cheese, then place the stacks on a baking sheet and place under the broiler to melt the cheese. Butter and toast the buns on both sides. Spread 1 tablespoon of the aioli on the bottom bun, top with a slice each of lettuce, onion and tomato. Repeat for the remaining buns. In a frying pan, fry the eggs over easy, and then place an egg on top of each stack. Then spread 1 tablespoon of the burnt olive relish on each top bun and place each top bun on a sandwich, and serve.
Consumption of raw or undercooked eggs, shellfish and meat may increase the risk of foodborne illness.