1. Melt 1 Tbsp. butter in a small nonstick skillet over medium-low heat; add 2/3 cup pecans, and cook, stirring often, 4 to 5 minutes or until toasted and fragrant.
2. Process flour and remaining 1/3 cup pecans in a food processor until finely ground; place flour mixture in a large shallow bowl.
3. Place chicken between 2 sheets of heavy-duty plastic wrap; flatten to 1/4-inch thickness, using a rolling pin or flat side of a meat mallet. Sprinkle chicken with salt and pepper; lightly dredge in flour mixture.
4. Melt remaining 2 Tbsp. butter with olive oil in a large nonstick skillet over medium-high heat; add chicken, and cook 2 to 3 minutes on each side or until golden brown and done. Remove chicken from skillet.
5. Add mushrooms and shallots to skillet; sauté 3 minutes or until mushrooms are tender. Add broth and Marsala to skillet, stirring to loosen particles from bottom of skillet. Bring mixture to a boil, reduce heat to medium, and cook, stirring occasionally, 5 minutes or until sauce is slightly thickened. Return chicken to skillet, and cook 1 to 2 minutes or until thoroughly heated.
6. Transfer chicken to a serving platter; spoon mushroom-Marsala mixture over chicken, and sprinkle with parsley and toasted pecans.