For the patties: Put the beef, tamari, dry mustard, garlic powder and onion powder in a mixing bowl. Use your hands to stir until just combined. Rest the mixture for 10 minutes and then shape it into four 6-inch patties.
Heat the olive oil in a large skillet over medium-high heat. Season the patties on both sides with the seasoning salt. Cook the patties until crisped and brown on the bottom, 4 to 6 minutes. Flip, top each with a slice of pepper Jack and cook until the bottoms are browned and the cheese melts, an additional 4 to 5 minutes.
For the French toast: Preheat the oven to 350 degrees F. with a rack set in the middle of the oven. Put the bacon on a cooling rack set over a baking sheet and cook until crispy, 10 to 15 minutes. Halve 4 of the slices and crumble the remaining 2 slices into a medium bowl.
Meanwhile, use your hands to crush the potato chips into rough crumbs (you can crush them into finer crumbs if you prefer) and toss them with the crumbled bacon. Using a 3-inch round cutter, punch out the centers of the bread slices. (Each round should weigh 20 grams.) Whisk the egg whites, almond milk and maple syrup in a mixing bowl or baking dish.
Heat a large non-stick skillet over medium heat and coat with cooking spray. In batches, dip the bread rounds in the egg white mixture to coat completely and then roll them in the crushed potato chips to cover. Cook until golden brown on both sides, about 2 minutes per side. Transfer the French toasts to a plate.
For assembling the burgers: Heat a medium skillet over medium heat and spray with cooking spray. Add the onion and cook, stirring occasionally, until completely softened and caramelized, 20 to 25 minutes.
When the onions are done, heat the olive oil in a medium non-stick skillet over medium heat. Add the eggs and cook until the whites have set but the yolks are still runny, about 2 minutes.
To build the burgers: On each slice of French toast layer 2 slices of tomato, 1 piece of lettuce, folded, 1 burger patty, 2 bacon halves, a spoonful of caramelized onions and an egg. Top with another slice of French toast and dust with powdered sugar.