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.
Process flour and remaining 1/3 cup pecans in a food processor until finely ground; place flour mixture in a large shallow bowl.
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.
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.
Add mushrooms and shallots to skillet; saut 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.
Transfer chicken to a serving platter; spoon mushroom-Marsala mixture over chicken, and sprinkle with parsley and toasted pecans.
