Remove the chicken breasts from the bone. Slice each breast in half lengthwise. Put them between pieces of plastic wrap and pound them with a mallet or a small skillet until they are 1/4-inch thick.
Set up a breading station with three pie plates or shallow dishes. Put the flour in one and season it with a generous pinch of salt and pepper, the eggs beaten with 2 tablespoons of water in another, and the breadcrumbs in the third. Dredge the chicken pieces in the flour, then the egg wash, then the breadcrumbs. Set aside. In a large skillet over medium heat, add the oil. When the oil is hot, add the chicken in 1 layer and cook until it is golden brown and crispy, about 4 minutes per side. Drain on brown paper and keep warm while you make the sauce.
In another skillet over medium heat, add the butter. When it is melted, add mushrooms and season them with salt and pepper. Cook until they are browned, about 6 minutes. Add the garlic and cook for 30 seconds then add the stock and simmer for 4 minutes and reduce by one third. Add the Worcestershire sauce, turn the heat off, and let cool for a minute before stirring in the sour cream. Serve the Schnitzel with the sauce poured over the top, garnished with parsley.