Pat pineapple rings with a paper towel and place in a resealable sandwich bag. Add ¼ cup of teriyaki sauce and toss until pineapple is well coated. Set aside.

Using a medium bowl, combine the ground beef, eggs, onion, garlic, soy sauce, bread crumbs, pepper, salt, and cayenne pepper. Mix until well combined.

Shape mixture into 6 patties. (Tip: Make the patties slightly thinner in the center. This will give the burger a better shape once cooked.)

Place burgers in a glass baking dish and pour remaining ½ cup of teriyaki over burgers. Let marinate for 15 minutes, turning once.

Preheat grill to medium-high heat.

Remove burgers and pineapples from teriyaki sauce and discard sauce.

Grill burgers on medium-high heat for 5 minutes.

Flip burgers and grill for 4-5 more minutes, or until fully cooked. At the same time, add pineapple rings and ham steak to grill and cook for 4-5 minutes, or until heated through.

Layer bottom buns with lettuce and onion. Add burgers and top with Swiss cheese, grilled pineapple and ham.