Lay bread on a plate and spread Dijon mustard on one or both slices. Place cheese slices on top.
If using grated cheese, add that now. Top with remaining slice of bread.
Heat skillet over medium heat. Once hot, add 1 teaspoon of butter and swirl the skillet to coat. Turn heat down to medium low or low.
Place the sandwich onto the skillet. Cook about 2 minutes, until bread is brown. (If you have a lid, you can cover the pan, which will help melt the cheese. Check frequently, since it will also brown more quickly.)
Remove the sandwich from the skillet with a pancake turner and set on plate. Add the remaining teaspoon of butter, melt and swirl to cover. Return sandwich to skillet on the other side to brown, another 2 minutes. Watch carefully and adjust heat as needed to prevent burning.