Sprinkle chicken breasts on all sides with salt, white pepper and nutmeg. In a large frying pan, heat together butter and oil. Add chicken breasts and brown lightly; turn, add mushrooms and shallots around chicken, and continue cooking until chicken breasts are lightly browned on both sides.
Pour on wine. Cover and simmer 15 to 20 minutes, just until chicken is cooked through. Using a slotted spoon, remove chicken to a warm. serving dish; keep warm. Bring liquid to boiling, stirring until reduced by about half (about 6 minutes). Mix in cheese, cream and paprika. Cook over moderate heat, stirring, until cheese melts and sauce is slightly thickened. Salt sauce to taste. Spoon over chicken. Garnish with cherry tomatoes and a sprinkling of green onions.