Cut the chicken in half lengthwise making two thinner pieces from each breast. Roll each piece in the seasoned flour, coating each side well.
In a heavy skillet, heat the oil and 1 1/2 tablespoon of the butter until sizzling over medium heat and cook the chicken in batches for about 12 to 13 minutes or until almost cooked through, turning halfway.
Place the chicken on a heated platter, and cook the mushrooms until lightly browned, about 5 minutes, stirring often. Add the garlic, and cook just until fragrant.
Add the broth and liqueur and turn up heat to medium high. Return the chicken to the skillet, and cook until the sauce reduces and begins to thicken, about 6 to 8 minutes.
Taste, and season with salt and pepper, and stir in the remaining butter until melted. Stir the parsley into the mixture and serve the chicken immediately on a platter, topped with the mushrooms and any remaining sauce.