In a shallow dish stir together flour, thyme, sage, salt, and pepper; set aside.
Place each chicken breast half between two pieces of plastic wrap.
Using the flat side of a meat mallet, lightly pound chicken to 1/4 inch thick.
Remove plastic wrap.
Dip chicken pieces into flour mixture, turning to coat.
In a large skillet, heat 1 tablespoon of the butter and the oil over medium-high heat.
Add chicken, and cook for 4-6 minutes, or until no longer pink, turning once.
Transfer chicken to a serving platter; cover and keep warm.
Meanwhile, whisk together any remaining flour mixture, broth, and Marsala; set aside.
Add mushrooms and shallot to now-empty skillet, and cook for 6-8 minutes, or until tender, stirring occasionally.
Gradually add Marsala mixture.
Cook until slightly thickened and bubbly, whisking regularly.
Whisk in the remaining 2 tablespoons butter until incorporated.
Serve sauce over chicken, and sprinkle with parsley.
Notes
Dried thyme: To use fresh herbs, you'll need 1 teaspoon each of fresh thyme and fresh sage.
Chicken breast halves: Chicken breast halves are sometimes called chicken cutlets. You can make a chicken breast half by slicing a chicken breast in half lengthwise.
Chicken broth: Chicken stock can also be used.
Marsala wine: You'll need dry Marsala wine, not sweet Marsala wine for this recipe.
Button mushrooms: Cremini mushrooms also work well.