Heat oven to 400º F.
Season the chicken with ½ teaspoon salt and ¼ teaspoon pepper. Roll up each cutlet with a slice each of the ham and cheese. Skewer with toothpicks.
Heat 2 tablespoons of the oil in an ovenproof skillet over medium-high heat. Add the roulades and cook, turning occasionally, until golden brown, 4 to 6 minutes.
Transfer the skillet to the oven and roast the roulades until cooked through, 8 to 10 minutes.
Meanwhile, in a large bowl, toss the greens, tomatoes, vinegar, remaining 2 tablespoons of oil, and ¼ teaspoon each salt and pepper.
Serve the roulades with the salad and mustard.