Preheat a large non-stick skillet over medium heat.
Spread 1 tablespoon of unsalted butter on one side of each slice of sourdough bread.
Place a slice of bread butter-side down onto the skillet. On the unbuttered side, spread a thin layer of Dijon mustard if you're using it, then layer it generously with several slices of roast beef followed by two slices of sharp cheddar cheese.
Top with another slice of bread, ensuring that the buttered side faces up. Cook this side for about 3-5 minutes until the bread turns golden brown and the cheese begins to melt.
Using a spatula, carefully flip the sandwich over and continue cooking for an additional 3-5 minutes until both sides are golden brown and crispy while ensuring that all the cheese has melted thoroughly.
Once done, remove the sandwich from the skillet and allow it to cool slightly before cutting it in half or quarters based on your preference.