Galliano, an Italian liqueur flavored with 30 herbs and spices, including anise and vanilla, gives the sauce for these stuffed chicken breasts a complex sweetness.
6 boneless, skinless chicken breast halves, pounded ⅛" thick
Kosher salt and freshly ground black pepper, to taste
12 tbsp. herbed goat cheese, softened
6 thin slices prosciutto
6 tbsp. unsalted butter, chilled
10 oz. cremini mushrooms, sliced
Flour, for dredging
2 tbsp. canola oil
1½ cups chicken broth
¼ cup Galliano liqueur
1 tbsp. finely chopped parsley
4 cups cooked rice, for serving
1. Season chicken with salt and pepper. Working with one breast half at a time, spread one side with 2 tbsp. goat cheese and top with one slice prosciutto; roll into a tight cylinder. Using kitchen twine, tie chicken roll 1" in from each end. Snip off excess twine.
2. Heat 3 tbsp. butter in a 12" skillet over medium-high heat. Add mushrooms and cook, without stirring, until browned, 4–5 minutes. Stir mushrooms and continue cooking until softened, about 8 minutes. Transfer to a plate; wipe out skillet. Put flour on a plate; dredge each chicken roll in flour. Heat 2 tbsp. butter and the oil in skillet over medium-high heat. Add chicken and cook, turning, until browned and cooked through, 12–14 minutes. Transfer chicken rolls to a plate. Add broth and Galliano to skillet; boil, stirring, until sauce has reduced by a third, 4–5 minutes. Return mushrooms and chicken to skillet; cook, turning to coat in sauce, until warmed through, about 5 minutes.
3. Transfer chicken to a platter. Remove skillet from heat; swirl in remaining butter to make a smooth sauce. Spoon sauce over chicken; sprinkle with parsley. Serve with rice.