Mix the jam, thyme, and salt and pepper to taste in a bowl. Lay out a long piece of plastic wrap on a cutting board. Place the chicken on the plastic and brush half of the jam mixture evenly on top of each breast. Mound a quarter of the cheese on each piece of chicken, then wrap 2 slices of ham around each breast to cover the cheese. Place another piece of plastic over the chicken and gently pound with a mallet or heavy skillet until about 1/4 inch thick. Heat 2 tablespoons olive oil in a medium nonstick skillet over medium-high heat. Add the chicken and cook until golden and crisp, 3 to 4 minutes. Turn and cook on the other side until cooked through but still moist, 3 to 4 more minutes. Meanwhile, whisk the shallot, mustard, vinegar and the remaining jam mixture in a medium bowl. Slowly whisk in the remaining 3 tablespoons olive oil to make a smooth dressing. Place each piece of chicken on a plate and drizzle with dressing. Toss the greens with the remaining dressing; serve with the chicken.
Photograph by Antonis Achilleos
Courtesy of Food Network Magazine