Trim the fat off the chicken breast and cut it in 4 pieces. First, cut off the tenderloin. Then cut the chicken breast in half front to back. Take the larger roundish piece and slice it in half lengthwise. Use a meat mallet to flatten the pieces to about 1/4 inch think.
Season each piece with salt and pepper to taste. Coat the chicken pieces with flour, shaking off the excess.
Heat 1 tablespoon olive oil in a medium skillet over medium high heat. Cook the chicken breast in batches, about 3 minutes per side. You may need to add more olive oil between batches. Remove the chicken and set the pieces on a plate. Tent them with aluminum foil to keep them warm.
Heat 1 tablespoon olive oil and add the mushrooms. Cook until they start to shrink, about 3-5 minutes.
Add the shallots. Season with a pinch of salt and cook until soft, stirring often to prevent burning, about 2 minutes.
Pour in the sherry and deglaze the pan. Scrape up any bits that are stuck to the pan. Let simmer for about 1 minute.
Add the chicken stock and let it reduce by half, about 5 minutes. Add the half and half and butter.
Put the chicken back in, sliding them under the sauce. Be sure to add any juices from the plate as this is valuable flavor. Let it simmer about 2- 3 minutes.
Garnish with fresh parsley.