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 onion rings: Put the oil in a small saucepan over medium-high heat and heat to 350 degree F. on a deep-frying thermometer. Whisk together the rice flour, seltzer water and 1 teaspoon salt. The consistency should just thick enough to coat the onion rings.
Working in batches, coat each onion ring in batter and fry until crispy, about 1 1/2 minutes. Transfer to a plate.
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 the olive oil in a large skillet over medium-high heat and cook the turkey bacon until crispy, about 2 minutes per side. Transfer to a plate lined with paper towels.
Spray a non-stick skillet over medium-high heat with cooking spray and cook the eggs until all of the white has solidified but the yolks are still runny, about 2 minutes.
Building from the bottom to the top: Start by topping 1 French toast slices topped with the 1 slice tomato and 1 leaf lettuce, folded to fit. Top the lettuce with a burger, 1 fried egg, 2 strips of turkey bacon, 1 onion ring and 1 tablespoon of ketchup. Top with another slice French toast and lightly dust with confectioners¿ sugar. Build 3 more burgers with the remaining ingredients and serve immediately.