In large saute or fry pan, melt butter. While butter is melting, combine flour, salt and pepper in small bowl. Dip each piece of chicken in milk; shake off excess. Dredge chicken in flour mixture and add to fry pan. (I like to cut chicken breasts in half before coating.)
Saute chicken in butter over medium to medium-high heat until browned and cooked through, turning often. Add more butter as needed. (Be careful turning chicken so as not to break off any of the flour coating.)
Remove chicken from pan and place on platter. Keep chicken warm while making the sauce.
Turnheat to medium high and add the mushrooms; saute until cooked. With mushrooms still in the pan, deglaze with the wine, stirring to get all of the brown bits off the bottom of the pan. Turnheat to medium low and continue to cook sauce, stirring frequently, until sauce has thickened slightly.
(Note: Sauce should be tasted frequently, and more wine or butter can be added as necessary. If sauce does not thicken properly, add a little bit of flour and continue to stir.)
When sauce is ready, add chicken back to the pan and turn to coat.
Remove chicken to serving platter and top with remaining sauce. Decorate with parsley sprigs.