For the chipotle secret spread: Stir the mayonnaise, adobo sauce, ketchup, relish and Worcestershire together in a bowl to make the spread. Set aside.
For the panko-crusted avocados: In a medium pan over medium-high heat, add enough canola oil for deep-frying the avocado slices and heat until very hot.
Put the flour in one shallow bowl, the egg in a second shallow bowl and the breadcrumbs in a third. Season the avocado slices with salt and pepper. Dredge the slices first in the flour, then dip in the egg and coat with the breadcrumbs. Fry the avocado in batches until the panko turns golden brown, 3 to 5 minutes. Set aside on a plate lined with paper towels.
For the burgers: Mix the ground chuck and some salt and pepper together in a bowl with your hands. Form the meat into 4 thin 1/4-pound patties, each about 4 inches in diameter and 1/2 inch thick.
Heat a large cast-iron skillet or griddle over medium-high heat until very hot, at least 5 minutes. Add as many patties as will fit comfortably--do not crowd--and cook until the sides of the patties are opaque, 2 to 3 minutes. Flip each patty and top with a slice of American cheese if desired. Cook until the cheese begins to droop and melt at the corners and edges. Repeat with the remaining burgers and cheese.
Slather the bottom half of each bun with the chipotle spread, then top with 2 tomato slices, 3 fried avocado slices, 1 lettuce leaf, a cooked burger and 1 slice of onion. Finish with a top bun. Serve immediately.