Warm the peanut butter in a saucepan over medium-low heat, stirring, until loose, about 2 minutes. Reduce the heat to low; keep warm.
Divide the meat into 6 loose balls, then gently flatten into thin patties. Heat a large cast-iron 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 the burgers are well done, 4 to 5 minutes per side.
Meanwhile, melt the butter in another skillet over high heat. Place the buns cut-side down in the hot skillet, press them down slightly with another skillet and toast until golden, about 2 minutes. Put the burgers on the bottom buns and spread each with 1 heaping tablespoon warm peanut butter. Top with lettuce and tomato. Spread mayonnaise on the cut side of each top bun, then put on top of the burgers.
Photograph by Tina Rupp
Recipe adapted from Wheel Inn Drive-In, Sedalia, Missouri for Food Network Magazine