In a medium bowl, combine the ground beef with sea salt, black pepper, garlic powder, and dried oregano.
Shape the seasoned beef into one large, even patty about half an inch thick.
Cut the mozzarella string cheese in half crosswise to create two smaller sticks.
Dip the cheese sticks into the whisked egg, then coat them thoroughly with the almond flour, pressing gently to adhere.
Heat the avocado oil in a cast-iron skillet or non-stick pan over medium-high heat.
Place the beef patty in the skillet and cook for 4 to 5 minutes on the first side.
Flip the patty and place the breaded mozzarella sticks in the skillet next to the beef.
Cook for another 4 minutes, turning the cheese sticks occasionally until the almond crust is golden and the cheese is soft.
Lightly toast the whole grain bun in a separate pan or toaster until warm.
Layer the bottom bun with baby arugula and the beef patty.
Top the patty with the crispy mozzarella sticks and a generous dollop of marinara sauce before closing with the top bun.