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Place 3 tablespoons butter in a small glass measuring cup. Microwave butter at MEDIUM-HIGH 45 seconds or until melted. Let stand 1 minute. Skim foam from surface, and discard. (Mixture will appear separated.) Pour melted butter through a fine sieve over a small bowl, and discard the milk solids. Set the clarified butter aside.
Heat a large nonstick skillet coated with cooking spray over medium-high heat; add mushrooms, shallots, and garlic. Cook 3 minutes or until moisture evaporates; remove mushroom mixture from pan. Set aside.
Place each chicken breast half between 2 sheets of heavy-duty plastic wrap; pound to a 1/4-inch thickness using a meat mallet or rolling pin. Sprinkle both sides of chicken with 1/8 teaspoon salt and 1/8 teaspoon pepper. Place flour in a shallow dish; dredge chicken breast halves in flour.
Add clarified butter to pan, and place over medium-high heat. Add chicken; cook 3 minutes on each side or until lightly browned. Remove chicken from pan. Return mushroom mixture to pan; add broth and Marsala, scraping pan to loosen browned bits. Bring mixture to a boil, reduce heat, and simmer 5 minutes or until reduced to 1 cup. Stir in peas; cook 1 minute. Add 1 tablespoon butter, half-and-half, 1/8 teaspoon salt, and 1/8 teaspoon pepper, stirring until butter melts. Return chicken to pan; cook until thoroughly heated. Serve chicken and sauce over pasta.