Preheat a panini style grill. Lightly grease with nonstick spray.
Stir in the broth, kitchen bouquet, and thyme to a saucepan over medium heat. Bring to a simmer (turn the heat down to medium low if needed) until the broth builds and concentrates in flavor. Stir in the flour/water mixture until fully combined. Dip the turkey in and simmer for 1 to 2 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 turkey.
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.