Combine mustard, sour cream, and Parmesan cheese in a small bowl.
Spread 2 teaspoons mustard mixture over each bread slice. Top each of the 4 bread slices with 4 ham slices, 2 tomato slices, 2 cheese slices, and 1/2 teaspoon fresh chives. Top with the remaining bread slices. Lightly coat outside of bread with cooking spray.
Heat a large nonstick skillet over medium heat. Add 2 sandwiches to pan. Place a cast-iron or heavy skillet on top of sandwiches; press gently to flatten. Cook 3 minutes on each side or until cheese melts and bread is toasted (leave cast-iron skillet on sandwiches while they cook). Repeat with the remaining sandwiches.