Rossini Burger

Shape beef into four 1"-thick patties; transfer to a plate. Season patties with salt and pepper; set aside.

Heat oven to 200˚. In a bowl, whisk cornstarch with 2 tbsp. demi-glace; set aside. Heat oil in a 12" cast-iron skillet over medium-high heat. Add burgers; cook, flipping once, until browned and rare, about 6 minutes. Place burgers on a baking sheet; bake until medium rare, about 5 minutes. (This helps keep the burgers juicy.) Transfer to a plate. Meanwhile, discard fat from skillet; return to medium-high heat. Add madeira; cook, scraping browned bits from pan, until liquid is nearly evaporated, 1-2 minutes. Add remaining demi-glace; boil. Reduce by a third, 1-2 minutes. Stir in cornstarch mixture; cook until thickened, about 1 minute. Set sauce aside.

Butter buns with 2 tbsp. butter; toast on a baking sheet in oven. Heat a 12" skillet over medium heat. Season foie gras with salt and pepper; sear, flipping once, until browned, about 2 minutes. Transfer foie gras to paper towels. Whisk fat from skillet into reserved sauce.

Melt remaining butter in a 10" skillet over medium heat. Add truffles; cook until hot, about 30 seconds. To assemble burgers, place a patty on each bun bottom; drizzle with a little sauce. Top each burger with a slice of foie gras and a few truffle slices. Sprinkle salt over the top; add top half of bun.