Make the patties. Combine 1 lb ground beef with ½ cup shredded carrots, ½ cup grated onion, 1 ½ tablespoon soy sauce, 2 teaspoon corn starch, ¼ teaspoon corn starch, ¼ teaspoon Chinese 5 spice powder, and salt in a large bowl. Mix until all the ingredients are fully incorporated. Shape patties into 4 equal patties and chill for 30 minutes.

Dust both sides of patties with rice flour, shaking off excess.

Heat oil and butter in nonstick skillet over medium-high heat. Add the patties to the pan and cook until browned, about 3 minutes. Flip over and cook on the other side until cooked, about 2 more minutes. Remove from heat and repeat with remaining patties. Set aside and keep warm.

In the same pan, add the Canadian bacon and cook until lightly browned, about 2 minutes. Remove from heat and set aside.

Wipe pan clean with paper towel. Heat 1 tablespoon oil. Crack eggs into the pan and fry until the desired degree of doneness. Remove from heat and set aside.

Assemble burgers by spreading the Japanese mayo and ketchup on both the top and bottom buns. Place a piece of lettuce on the bottom bun followed by the tomatoes, cucumber, beef patty, bacon, fried egg. Top with remaining bun. Serve.