Form beef into 8 thin, oval-shaped patties. Spread 4 patties with French mustard, and season generously with salt and freshly ground black pepper. Place a slice of cooked ham on each patty, trimming away excess ham. Place ham scraps on top of ham slice and top with remaining patties, pressing meat firmly together.
Sauté patties in equal quantities of butter and olive oil for 2 or 3 minu