Prosciutto-Wrapped Chicken with Mushroom Marsala

4 large boneless, skinless chicken thighs (about 1 1/4 pounds), trimmed
1/2 teaspoon freshly ground pepper, divided
4 thin slices prosciutto (about 2 ounces)
4 teaspoons extra-virgin olive oil, divided
1 large shallot, halved and thinly sliced
1 tablespoon finely chopped fresh oregano plus 1 teaspoon, divided
8 ounces sliced cremini mushrooms
1/2 cup Marsala (see Tip) or dry sherry
1 cup reduced-sodium chicken broth
2 teaspoons cornstarch

Sprinkle chicken thighs with 1/4 teaspoon pepper and wrap each with a slice of prosciutto.

Heat 2 teaspoons oil in a large nonstick skillet over medium-high heat. Add the chicken and cook, turning once, until browned on both sides and cooked through, 4 to 5 minutes per side. Transfer to a plate; tent with foil to keep warm.
    
Reduce heat to medium and add the remaining 2 teaspoons oil, shallot and 1 tablespoon oregano to the pan. Cook, stirring, until the shallot is beginning to brown, 1 to 2 minutes. Add mushrooms and cook, stirring, until browned in spots, 4 to 6 minutes. Add Marsala (or sherry), return heat to medium-high and cook 2 minutes.
    
Whisk broth, cornstarch and the remaining 1/4 teaspoon pepper in a measuring cup; add to the pan, stirring. Return to a simmer and cook, stirring constantly, until the sauce is thickened and glossy, about 4 minutes. Serve the chicken with the mushroom sauce, sprinkled with the remaining 1 teaspoon oregano.

Per serving: 310 calories; 15 g fat ( 3 g sat , 7 g mono ); 87 mg cholesterol; 10 g carbohydrates; 0 g added sugars; 28 g protein; 0 g fiber; 588 mg sodium; 513 mg potassium