Preheat your grill to medium heat.
Take your sliced brisket and heat it up on the grill for a few minutes until it is hot and slightly crispy.
Butter one side of each slice of sourdough bread.
On the non-buttered side of one slice of bread, place a slice of cheese.
Add the hot brisket on top of the cheese, making sure it covers the whole slice of bread.
Add the second slice of cheese on top of the brisket.
Place the other slice of bread on top of the cheese, the buttered side facing up.
Place the sandwich on the grill and cook for 2-3 minutes on each side, until the bread is crispy and the cheese is melted.
Remove the sandwich from the grill and let it cool for a minute or two before cutting it in half.
Serve hot and enjoy your delicious brisket grilled cheese sandwich!