Melt the butter in a skillet. Add the onion and carrot and cook until lightly browned, about 5 minutes.
Stir in the flour and cook until brown. Add the beef broth, bay leaf, pepper, and salt, and simmer for 10 - 15 minutes. Strain, then add the Madeira and chestnuts and set aside.
Preheat the broiler.
Place the venison steaks on a rack 5 inches beneath the broiler element. Cook 5 minutes on each side.
Remove steaks to a hot platter and cover with the hot chestnut sauce.