Sprinkle chicken with 1/4 tsp salt and pepper. In a skillet, cook chicken in 2 Tbsp oil over medium heat for 6-8 minutes on each side or until a thermometer reads 170 degrees. Remove and keep warm.
In the same skillet sauté mushrooms in remaining oil until tender. Add garlic; cook one minute longer.
Add wine, stirring to loosen browned bits from pan. Bring to a boil; cook until liquid is reduced by a third. Stir in cream and remaining salt. Return to a boil; cook until slightly thickened.
Return chicken to pan; add 1/3 cup cheese. Cook until cheese is melted. Sprinkle with remaining cheese; garnish with parsley.
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