For Mushroom Stuffing, Heat vegetable oil in a skillet.
Sauté chopped onion with garlic in the skillet over medium-high heat for 1 minute.
Add chopped mushrooms, and cook until the mushrooms have released their juices and the juices have evaporated (about 7 minutes).
Add minced scallion, oyster sauce and rice vinegar and continue cooking for another 2 minutes.
Cool completely before stuffing and cooking the burgers.
For Hamburgers, combine ground chuck, scallion, ginger, garlic, soy sauce, teriyaki sauce and black pepper in a bowl.
Form meat into 8 thin patties, 3/8-inch thick.
Place an equal amount of mushroom filling on half of the patties, leaving a margin around the edge.
Cover the stuffing with the remaining patties.
Seal the edges by pressing them together with your fingers.
Preheat grill to medium-high and grill the patties uncovered for 2-1/2 to 3-1/2 minutes per side for charcoal grills (3-1/2-4-1/2 for gas grill), flipping once, until internal temperature reaches 160 F.