Shape 1 kg ground beef into 4 patties of roughly 250 g each.
Coat the patties with 3 tablespoons teriyaki sauce, dividing the amount equally among all patties on both sides. Refrigerate for 15 minutes.
In a saucepan over low heat, combine 1 cup tomato ketchup, 1 cup brown sugar, and 3 tablespoons mustard. Stir continuously until the sugar dissolves, about 3-5 minutes. Set aside.
Heat a grill or pan to medium-high heat. Cook the patties for 3-4 minutes on the first side. Flip the patties, add sliced onion around them, and season with salt and pepper. Cook for another 3-4 minutes until the patties reach an internal temperature of 71°C (160°F) and the onions are soft and browned. Spread the special sauce over the patties and onions, reduce heat to low, cover, and cook for 2 minutes.
Cut burger buns in half. Toast the cut sides in a 180°C (350°F) oven for 3-4 minutes until lightly golden.
On the bottom half of each bun, layer: salad, burger patty with sauce and onions, Gouda cheese, tomato slice, pineapple slice, and top bun.