Preheat a panini style grill. Lightly grease with nonstick spray.
Melt the butter in a saucepan on medium heat. Stir in the flour until fully combined and until golden brown. Then stir in the broth, kitchen bouquet, and thyme. Bring to a simmer (turn the heat down to medium low if needed) until the broth reduces and thickens to a smooth consistency and concentrates in flavor. Add the beef in and simmer for a few minutes so it soaks in the flavor, then remove with a slotted spoon and place on the bread. Continue simmering the liquid on low.
Layer the bread with cheese and beef.
Place the sandwich on the panini style grill and cook until golden brown on both sides and the cheese is melted.
Cut the sandwich in half, serve with chips, pickle, and gravy for dipping on the side.