Combine crushed green pepper with 4 tablespoons butter. Set aside.
Place fillets between plastic wrap and pound gently. Insert a knife on one side of the chicken breast. through the center. Move knife back and forth in order to create a pocket. Do the same with remaining chicken breast halves. Introduce the green pepper mixture in each pocket and spread it evenly. Place fillets in a bowl and marinate in brandy for 30 minutes, turning once. Remove from marinate, dry and season with salt and pepper. Save the marinade.
Melt 2 tablespoons butter with oil and add chicken fillets to brown. Remove fillets and deglaze skillet with the brandy from the marinade, scraping bottom of pan with a wooden spoon. Bring mixture to boil, add chicken stock and wine and reduce for 5 minutes.
Transfer to a bowl.
Melt remaining butter in the same skillet and sauté green onion until soft. Stir in the chicken stock mixture, return chicken fillets to the skillet and bring to a boil until chicken is tender. Stir in 2 tablespoons flour diluted in cold water to thicken sauce, if desired.
Stir in heavy cream before serving.