Combine ground beef with 1/4 cup of steak rub in a bowl.
Add eggs, diced onion and oats. Mix until well combined.
Cut mozzarella block into a 5 ounce chunk.
Mold ground beef mixture into a loaf.
Make a well in the center of the ground beef and place the mozzarella inside.
Form the ground beef around the mozzarella.
Prepare a grill fire to 320° using hickory or pecan for smoke flavor.
Place the meatloaf over indirect fire. Sprinkle the top with 1 tablespoon steak rub. Cook with the grill closed for 45 minutes.
Meanwhile, mix the tomato sauce with balsamic vinegar, brown sugar, basil, thyme, oregano, salt and pepper.
Top the meatloaf with about 1/2 of the tomato sauce and continue to cook another 15 minutes.
Check internal temperature of meatloaf, near the center and continue to cook until meatloaf reaches 160°.
Remove from grill to a serving platter. Rest 10 minutes before slicing and serving. Serve with remaining tomato sauce if desired.