Place each chicken breast half between 2 pieces of plastic wrap. Using the flat side of a meat mallet, lightly pound chicken to 1/4-inch thickness. Remove the plastic wrap. In a shallow dish, combine flour and pepper. Coat chicken pieces with flour mixture.
In a very large skillet, cook the chicken in 2 tablespoons of hot butter over medium heat for 6 minutes or till the chicken is no longer pink, turning once. Remove from skillet, reserving drippings in skillet. Transfer the chicken to a serving platter and keep warm.
Add green onion to the drippings in the skillet. Cook and stir for 1 to 2 minutes or till the onion is tender. Stir in whipping cream, white wine or broth and mustard. Cook and stir for 1 to 2 minutes or till the mixture is smooth and slightly thickened. Spoon sauce over chicken. Garnish with thyme sprigs, if you like.