Spread the softened butter on the cut side of the hamburger buns and toast under the broiler until just browned. Set aside.: The moment you slide the buns under the broiler you will smell warm, toasty butter and see the edges develop a light golden color, which gives a slight crispness that holds up to the juicy patty. This step is about texture, it prevents soggy bottoms and adds a toasty aroma that makes the first bite inviting. If the buns are under the broiler too long they can brown too fast, so watch constantly and pull them when they are just kissed with color. A common error is stepping away and returning to overly dark buns, which can taste bitter. Use a shallow baking sheet so the cut sides face the heat evenly, and leave the buns to rest while you prepare the other components so the warmth redistributes.
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.: As you gently fold the ground chuck with the seasoning and teriyaki glaze , you will notice the meat take on a glossy sheen and a more aromatic profile from the pepper and salt. Forming the patties by hand, press them just enough to hold shape while keeping some air pockets, which yield a tender result. This blending step infuses flavor throughout the patty instead of just on the surface. Overmixing will toughen the texture, so stop when it is evenly combined. For consistent cooking, aim for uniform thickness across all patties. If the meat feels sticky, a light chill for 10 minutes helps it firm up for better searing.
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.: When the pineapple rings hit the hot surface you will hear a gentle sizzle and soon see the sugars caramelize into attractive brown lines, releasing a warm tropical scent that fills the kitchen. That browning transforms brightness into a deeper sweetness that balances the savory patty. Once browned, transfer them so they stay intact and do not overcook, which would make them mushy. If you use a skillet, wiping it clean before cooking the patties prevents residual sugars from burning when the meat hits the pan. A typical misstep is cooking at too high heat, which chars the fruit rather than caramelizing it; medium heat gives the best color and texture.
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.: As the patties sear you will hear a lively sizzle and see a rich brown crust form, that Maillard crust locks in juices and gives deep savory notes. Brushing the reserved teriyaki glaze introduces glossy sweetness and enhances caramelization on the exterior. When you add the cheddar cheese and cover the skillet, steam helps the cheese soften into a melty blanket, creating a smooth transition between beef and toppings. Use a thermometer to hit your desired doneness rather than relying solely on time if you want precision. A frequent mistake is flipping too often, which prevents a proper crust from forming, so let the patties sear undisturbed until they release easily from the surface.
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.: The moment you assemble you notice the layered textures and aromas coming together, the creaminess of mayonnaise marrying with the warm, glazed patty and smoky-sweet pineapple . Layering matters here, placing the cheddar cheese melted patty directly on the bottom bun creates a stable base while the pineapple and tomato add moisture and brightness, and the shredded lettuce contributes crisp contrast. Press gently to keep everything in place, then serve immediately so the cheese remains gooey and the bun retains its toastiness. A common pitfall is assembling too early, which lets steam soften the bun and wilt the lettuce, so build just before serving.