Prep the cheese: Cut the mozzarella into three rectangular logs, each about 3 inches long and 1 inch thick. Place on a plate and freeze for exactly 30 minutes.
Mix the meat base: In a large bowl, combine panko and milk. Let it sit for 2 minutes until the panko absorbs the milk. Add the egg, Parmesan, grated onion, garlic, salt, pepper, and oregano. Mix with a fork or your hands until just combined — do not overmix.
Assemble the loaf: On a piece of parchment, pat the meat mixture into a 10x6 inch rectangle about 3/4 inch thick. Place the three chilled cheese logs end-to-end in the center. Use the parchment to lift and roll the meat over the cheese, sealing the edges and ends completely.
Glaze and bake: Place the loaf seam-side down on the baking sheet. Mix the ketchup, brown sugar, and mustard, then spread evenly over the top and sides of the loaf. Bake at 375°F for 45-50 minutes, until internal temp reaches 160°F.
Rest before slicing: Let the loaf rest for 10 minutes before slicing. If you cut too early, the cheese will run out. After the rest, slice into thick pieces and watch the cheese pull.