Set out a heavy skillet or cast iron griddle. Beat the eggs slightly in a pie tin or shallow bowl and add the milk or cream and salt, set aside. Spread the bread slices out on a flat working surface. Spread one side of four slices of bread lightly with the prepared mustard. Top each with a slice of cheddar cheese. Butter the remaining four slices of bread and top each cheese slice with bread, butter side down. Heat the butter in the skillet or on the griddle. Carefully dip each sandwich into the egg mixture, coating both sides. Allow the excess egg mixture to drain back into the bowl. Dip only as many sandwiches as will lie flat in the skillet or griddle. Cook over low heat until browned. Turn and brown the other sides. Repeat for the remaining sandwiches and if necessary, add more butter to the skillet or griddle to prevent sticking. Or you can place the sandwiches, after dipping, on a well greased baking sheet and brown in the oven at 450 degrees F. for 8 to 10 minutes. Serve hot.