Preheat an outdoor grill or grill pan to medium-high heat.
Place the ground beef in a mixing bowl. Season lightly with salt and black pepper.
Add a small portion of the teriyaki sauce to the beef, reserving most of the sauce for brushing and serving. Mix gently until just combined.
Divide the mixture into four equal portions and shape them into patties slightly wider than the burger buns.
Make a shallow indentation in the center of each patty with your thumb to encourage even cooking.
Place the patties on the hot grill and cook for approximately 4–5 minutes on the first side.
Flip and continue grilling until the burgers reach your preferred doneness. For food safety, ground beef should reach an internal temperature of 160°F (71°C).
Brush the patties with some of the reserved teriyaki sauce during the final minutes of cooking. Do not use sauce that has contacted raw meat.
If using cheese, place one slice over each patty during the final minute and allow it to melt.
Meanwhile, place the pineapple rings on the grill. Cook for 2–3 minutes per side, until warm, caramelized, and marked by the grill.
Place the cut sides of the buns on the grill for 1–2 minutes, until lightly toasted.
To assemble each Hawaiian Teriyaki Pineapple Burger, spread spicy mayo or another preferred condiment over the bun, if desired.
Layer the bottom bun with lettuce, tomato, a grilled burger patty, and one caramelized pineapple ring.
Spoon or brush with additional clean teriyaki sauce as desired.
Add the top bun and serve immediately.