Preheat the oven to 400 degrees F. Chip the top bit off of the head of garlic, exposing the cloves. Don't worry about the skin. Place in an aluminum foil packet and drizzle with olive oil. Sprinkle with salt and bake for 40 minutes.
When cool enough to handle, squeeze the garlic from the skin and pulse in a food processor. Add the mayo, and pulse until combined. Season with salt and pepper if needed. Store in an airtight container in the fridge for up to 3 days.
Meanwhile, preheat your grill for medium-high. Clean and grease the grates.
Mix the ground beef, Worcestershire sauce, Montreal Steak seasoning, and salt and pepper in a bowl. Form into even patties with an indent from your thumb in the center.
Drizzle a little more olive oil in a large skillet over medium heat and cook the peppers and onions until soft and starting to brown, 8 to 10 minutes. Set aside.
Place the burgers on the preheated grill and cook until done, 5 to 7 minutes, flipping once halfway through. Cover with cheese, close lid and let the cheese melt, a minute longer.
Arrange the burgers on toasted buns with the garlic mayo, lettuce, peppers and onions. Serve warm and with napkins.