MaKe the Shoestring Fries: Heat oil to 375 degrees F. Slice the potatoes lengthwise into 1/8-inch slices. Then cut each slice into 1/8-inch long strips. Add the strips in batches, separating them when they hit the oil. Fry until golden brown, remove and drain on paper towels and season with salt.
Make the Burgers: Divide the meat into four equal portions (6-ounces each). Form each portion into loosely into a 3/4 -inch burger and make a deep depression in the center with your thumb. Season both sides of each burger with salt and pepper.
Cook the burger until slightly charred on both sides and cooked to desired doneness. Add the American cheese, during the last minute of cooking. Remove the burgers to a plate and loosely tent.
Reduce the heat of the pan/griddle to medium heat. Crack the eggs onto the cooking surface you used for the burgers and season the tops with salt and pepper. Let the eggs cook until the white just sets up, about 45 seconds. Gently flip the eggs over (trying not to break the yellow) and cook for 10 seconds. Place the eggs on top of the cheese on the burger. Place the burgers on a bun and top with the bacon and some of the shoestring fries. Drizzle fries with chipotle ketchup.