Preheat your outside grill with lid closed to medium-high heat. While preheating, in a small bowl mix the basting liquid throughly with a whisk.
Cut the chicken breasts by starting at the thin side of the breast. Do not cut all the way through. Try to make a pocket that can easily be sealed with toothpicks.
Coat the inside of each chicken breast with a tablespoon of Dijon mustard. Use a knife or spatula.
Divide the cheese into four groups and roll inside the four ham slices. Try to surround the cheese as much as possible with the ham. Insert one ham and cheese group inside the pocket of each chicken breast. Seal each breast with toothpicks.
Grill the chicken for 6-8 minutes, with the lid down. Flip the breast, and again cook for 6=8 minutes. Do not move around. Turn heat down to medium-low. Flip once more and baste with liquid and cook with lid up for 2 minutes. Flip again and baste the other side, cooking for 2 minutes. Watch for flare-ups. Chicken should be done on the inside and somewhat crispy on the ourside. Remove the toothpicks before serving.
Combine all of the ingredients (except for the butter and thyme) in a saucepan and bring to boil over medium heat. Stir and simmer for 10 minutes, while the chicken is grilling, and until thickened. Add the butter and melt at the end for a glistening sauce. Sprinkle the finished chicken with chopped thyme leaves before serving. Allow guests to pour the mustard sauce over the chicken or serve on the side.
We find that the portions are actually large enough that you can actually have 8 servings. We have computed the nutrition based upon 4 servings. You can cut the numbers in half if you serve half portions. Ham slices are usually thin - you can add more ham if you prefer. Just make sure the ham covers the cheese.