Generously butter the flat sides of the burger buns. Set aside.
In a large bowl, use your hands to combine the brisket, chuck, salt, garlic powder and pepper. Divide the mixture into 8 even portions and form into patties.
Heat a cast-iron griddle or skillet over high heat and brush with butter. Put the burgers on the hot griddle and season with a sprinkle of salt. Cook until browned, about 2 minutes, then flip and top each with a slice of Cheddar and a slice of American (form a "star" with the cheese slices so the cheese completely envelopes the burger patty). Cook, using a large metal bowl to dome the burgers and allow the cheese to melt, 1 to 2 minutes. Transfer the burgers to a baking sheet and dome with the bowl to keep hot. Place the buns on the griddle butter-side down to quickly toast.
Place the patties on the bottom buns and top with onions, tomatoes, pickles and a pile of lettuce. Spread a generous dollop of mayo on the top buns and place the buns on the burgers. Eat and enjoy!