Combine mayo, sour cream, minced chipotle peppers, freshly minced cilantro, and lime juice in a bowl, then stir in 1½ tsp fajita seasoning until well blended. Set aside. While the aioli rests, prepare all your toppings: shred the romaine lettuce, slice the red onion into thin rings, slice the tomatoes, cut the avocado into wedges, and toast your brioche buns with butter until golden. I prefer to season my aioli at least 10 minutes ahead so the flavors meld together beautifully.
Divide the ground beef into 8 equal balls, handling the meat gently to avoid overworking it. In a small bowl, combine 1 tbsp fajita seasoning with 1 tsp garlic powder to create your seasoning blend. Have this ready next to your cooking station along with the 8 slices of Monterey Jack cheese.
Heat canola oil in a large skillet over high heat until it begins to smoke—this ensures a proper crust. Working in batches to avoid crowding, place a beef ball in the pan and immediately use a spatula to press it firmly into a thin, flat patty (about ¼-inch thick). Season the cooked side generously with your seasoning blend and cook for 2 minutes without moving the patties. The high heat creates that crucial caramelized crust for flavor.
Flip each patty carefully and season the second side with your seasoning blend. Immediately top each patty with one slice of Monterey Jack cheese. Add about 2 tablespoons of water to the skillet, cover with a lid, and let it steam for 10 seconds—just enough time for the cheese to melt completely. Stack two cheesy patties together to form each burger, then transfer to a plate. I find that stacking the warm patties while they're still steaming helps the cheese bond them together perfectly.
Place the bottom halves of your toasted brioche buns on a work surface. Layer shredded romaine lettuce, sliced tomatoes, and red onion rings on each bottom bun. Set a stacked beef patty (with melted cheese) on top of the vegetables. Arrange avocado slices on top of the beef patties, then spread a generous amount of the chipotle aioli from Step 1 on the top bun halves. Close the burgers gently and serve immediately.