Preheat oven to 200 degrees C. Cut a cross in the skin of the chestnuts, place in a baking pan and bake for 15 minutes. Remove from oven and cool. Peel off the shell and chop. You should have about 1 cup chopped chestnuts.
Melt butter in a large frypan over medium heat. Cook the onions and carrots in the butter until soft, stirring often. Stir in the flour and cook until the flour browns. Mix in the broth and season with bay leaf and salt and pepper. Simmer for 15 minutes.
Preheat grill and position rack 12cm below the heat source. Place the venison steaks in a grill pan. Cook 5 minutes on each side. Transfer to a plate kept warm in the oven.
Strain the solids from the broth and return the broth to the pan. Stir in Madeira and chestnuts. Pour hot chestnut sauce over venison steaks and serve.