Mix the jam, thyme, S&P to taste, in a bowl. Lay a long piece of plastic wrap on a cutting board. Place the chicken on the plastic and cover with another piece. Gently pound with a mallet to about 1/4" thick.

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 covering the cheese.

Heat 2T oil in a medium nonstick skillet over medium-high heat. Add the wrapped chicken and cook until golden brown and crispy, 3-4 minutes each side. Meanwhile, whisk the shallot, mustard, vinegar and remaining jam mixture in a medium bowl. Slowly whisk in the remaining 3T olive oil to make a smooth dressing.

Place each piece of chicken on a plate and drizzle with some of the dressing. Toss the greens with the remaining dressing; serve with the chicken.