Preheat the broiler. Melt 2 tablespoons butter in a large cast-iron skillet over medium heat. Add the onions and cook until translucent, 6 to 8 minutes. Add 1/3 cup water, cover and continue cooking until the onions are golden brown, about 15 more minutes. Season with salt and pepper. Transfer the onions to a bowl and wipe out the skillet.

Divide the meat into 6 loose balls, then gently flatten into thin patties. Heat the skillet over high heat. Add the patties to the hot skillet, smash them flat with a spatula and season with salt and pepper. Cook, flipping once, until well done, about 3 minutes per side.

Meanwhile, toast the buns under the broiler. Put the patties on the bottom buns and top each with 1/4 cup sauteed onions. Smear 2 tablespoons butter on the cut side of each top bun, then put on top of the burgers. Slice in half and serve immediately.

Photograph by Tina Rupp