Combine the onion, water and 1 tablespoon butter in a skillet over medium-low heat, cover and cook for 8 minutes.
Uncover the onions and cook for 4 more minutes until tender and lightly golden, then transfer them to a bowl.
Shape the beef into 4 loose patties wider than the buns and season both sides with the salt and pepper.
Melt 2 tablespoons butter on a griddle over medium-high heat and toast the cut buns for 1 minute.
Cook the patties on the hot griddle for 4 to 5 minutes per side without pressing until they reach 160°F.
Lay American cheese on each patty for the final minute and cover briefly to melt it.
Spread the remaining 5 tablespoons softened butter thickly across the cut buns, then build each with a cheesy patty, warm onions and 3 pickle chips.
Serve immediately so the cool bun butter melts into the beef rather than pooling on the plate.
