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Step 1
Spread the softened butter on the cut side of the hamburger buns and toast under the broiler until just browned. Set aside.
Step 2
In a mixing bowl, combine the ground chuck, salt, pepper, and 2 tablespoons of teriyaki glaze. Mix until blended well. Form the mixture into 4 equally sized patties.
Step 3
Place the pineapple rings onto a grill pan or buttered iron skillet and cook over medium heat for a few minutes on each side until the pineapple rings begin to brown. Remove from the grill or skillet and set aside. If using a skillet, wipe it clean with a paper towel.
Step 4
Place the burger patties on the grill or skillet and cook over medium heat for 4 to 6 minutes on each side, until they reach your preferred level of doneness. Brush about 2 teaspoons of glaze onto each patty and top with cheddar cheese. Cover the skillet until the cheese begins to melt.
Step 5
To assemble the burgers, spread a bit of mayonnaise on both cut sides of each bun. Place a burger patty on the bottom bun. Then add 2 grilled pineapple rings, 2 tomato slices, and 1/4 cup shredded lettuce. Cover with the top bun.