Season chicken with salt and pepper
Working with one breast half at a time, spread one side with 2 tablespoons 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
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 Somerset Ridge Avalon 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
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 or bucatini pasta, and with Avalon Apples on the side