1. Divide the ground beef into two equal portions and flatten them into thin, wide patties on a piece of parchment paper.
2. Slice the mozzarella cheese stick into 0.5-inch rounds and arrange them in the center of one beef patty, leaving a margin around the edges.
3. Place the second beef patty over the cheese and pinch the edges of the two patties together firmly to ensure the cheese is completely sealed inside.
4. Season both sides of the stuffed patty evenly with sea salt, black pepper, and garlic powder.
5. Heat the avocado oil in a cast-iron skillet or non-stick pan over medium-high heat until shimmering.
6. Carefully place the patty in the skillet and sear for 4 to 5 minutes per side, or until the beef is cooked to your desired level of doneness and the cheese center is melted.
7. During the last minute of cooking, place the sprouted grain bun halves cut-side down in the skillet to lightly toast them.
8. Warm the marinara sauce in a small saucepan over low heat or in a microwave-safe bowl until bubbling.
9. Assemble the burger by placing the baby arugula and tomato slices on the bottom bun, followed by the stuffed beef patty, a generous pour of warm marinara sauce, and the top bun.