Trim fat and sinew from chicken breasts; pound to 1/2" thickness.
Heat 2 tbsp olive oil in large saute pan; cook chicken breasts about 5-6 minutes per side, or until nicely browned and cooked through; set aside and keep warm.
Slice mushrooms into pieces about 3/8" thick; have ready to saute.
Add mushrooms and cook until mushrooms become tender, 5 minutes or so, adding a little more butter if necessary; add rosemary just as mushrooms are becoming done.
Stir in dry sherry and cook for 30 seconds or so, stirring up any bits from bottom of pan; add the cream, half the parsley, the black pepper, and cook for 30- 45 seconds more, until warmed through.
Note: this sauce has sliced mushrooms in it, but if you prefer a creamier sauce, simply use a hand blender and puree the sauce in the pan and strain if desired, or pour it carefully into a blender and do the same.
To serve, place chicken on serving plate and spoon creamy rosemary sauce over chicken.