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Gather and measure all ingredients: ground Wagyu beef, kosher salt, black pepper, buns, cheese, lettuce, tomatoes, onion, pickles, condiments, and butter or oil.
Divide the 1.5 pounds of ground Wagyu beef into four equal portions, handling the meat as little as possible.
Form each portion gently into a patty about 3/4-inch thick and slightly wider than the buns, pressing a small indentation in the center of each.
Season both sides of each patty with 1 teaspoon kosher salt and 1/2 teaspoon freshly ground black pepper.
Heat a large cast iron skillet or heavy-bottomed pan over medium-high heat for about 3–4 minutes until very hot.
Add 1 tablespoon unsalted butter or neutral oil to the pan and swirl to coat.
Cook the patties without overcrowding the pan: 3–4 minutes per side for medium-rare, 5–6 minutes per side for medium, or until internal temperature reaches 160°F for well done.
About 1 minute before the end of cooking, place a slice of cheese on each patty, cover with a lid or foil for 30–60 seconds to melt.
While the patties rest, lightly toast the brioche or potato buns on a separate dry skillet or under the broiler until golden.
Transfer the cheesy patties to a plate and let rest for 5 minutes to redistribute juices.
Assemble burgers: spread ketchup, mustard, or aioli on buns, add a patty, then top with lettuce leaves, tomato slices, red onion, and dill pickles. Serve immediately.