Melt 1 tablespoon of the butter in a large skillet over medium heat.
Once the butter is melted, add the onions. Toss to coat all the onions in the butter, reduce the heat to medium-low and let the onions saute slowly for 30 minutes, stirring frequently. After 30 minutes they should perfectly caramelized.
Use the remaining tablespoon of butter to spread on one side of each slice of bread.
With the buttered side facing down, layer half the cheese slices on top of the bread, then lay the roast beef on top of the cheese, followed by 2 tablespoons of caramelized onions.
Top the onions with the remaining cheese and the grainy dijon mustard and then the other slice of bread with the buttered side facing up.
Transfer the sandwich to a skillet over medium heat and cook until the cheese is melted.
After 2 - 3 minutes, flip the sandwich over and repeat. The first side should be a nice golden brown.
Once the other side is golden brown and the cheese is melted, remove from the skillet, cut in half and serve.