In a shallow dish or bowl combine bread crumbs and 3 tablespoons flour. Dip chicken into ice water then coat with crumb mixture.
In a medium frypan heat oil over medium high heat. Add chicken and saute until both sides are lightly browned and chicken is cooked through (juices run clear). Remove chicken from frypan and set aside, keeping warm.
To same frypan add mushrooms and saute. Sprinkle with remaining 1 tablespoon flour and stir quickly to mix together. Add stock and wine and let simmer, stirring, until thickened (about 2 minutes).
Return reserved chicken to frypan. Top with cheese. Cover and cook until cheese is melted.