Preheat a cast-iron pan or griddle to at least 400°F.
Strongly season both sides of the patties with the salt-and-pepper mix.
Sear for one minute on each side until the crust is dark brown, then constantly flip the burgers to achieve an even exterior char until reaching an internal temperature of 130°F (medium rare).
Places two slices of American Cheese atop the patties and cover with a melting dome or pan lid until melted.
Remove the patties and rest for 3 minutes.
While the patties are resting, toast the buttered buns on the griddle/in the pan.
Lay the onion slice atop the heel (bottom) of the bun and place the burger patty on top.
Place the crown (top) of the bun on top of the burger and serve with cottage fries, a pickle, and ketchup.
Notes
The Red Hook Tavern burger is an ode to the (not quite as good) Lugar-Burger from nearby Peter Luger Steak House. Both restaurants are believed to source their sturdier, Italian-American bread-like buns from wholesale bakery Tribeca Oven (who also supply Luger's fabled onion rolls). Baker Keith Cohen, formerly of Tribeca Oven and current owner of New York institution Orwashers, makes a very similar Sesame Burger Bun at both Manhattan locations, the recipe for which can be found here.