Preheat a large skillet or griddle over medium heat.
In a small bowl, mix together the Dijon mustard, barbecue sauce, garlic powder, salt, and pepper. Spread this mixture evenly on one side of each slice of sourdough bread.
On the unspread side of four slices, layer 2 slices of cheddar cheese, followed by an even distribution of the shredded brisket, and then top with 2 more slices of cheddar cheese.
Place the remaining four slices of bread on top, spread side up, to form sandwiches.
Spread 1 tablespoon of softened butter on the outside of each sandwich.
Carefully place the sandwiches in the preheated skillet. Cook for about 4-5 minutes on each side, or until the bread is golden brown and the cheese is melted.
Remove from the skillet and let cool for a minute before slicing in half.