1. Pat chicken dry with paper towels and season with 1 teaspoon salt and 1/2 teaspoon pepper. Heat butter and oil in 12 inch skillet over medium high heat. When foaming subsides, place chicken in skillet and cook until browned, about 4 minutes. Flip chicken and continue to cook until browned on second side, about 4 minutes longer. Transfer chicken to large plate.
2. Add mushrooms, onion and wine to now empty skillet and cook stirring occastionally until liquid has evaporated and mushrooms are browned, 8-10 minutes. Add flour and garlic; cook; stirring constantly, 1 minute. Add broth and bring mixture to boil, scraping bottom of pan with wooden spoon to loosen browned bits. Add chicken and any accumulated juices to skillet. Reduce heat to medium low; cover and simmer until instant read thermometer registers 180 degrees when inserted in breasts and 175 degrees when inserted in thighs (8-10 minutes).
3. Transfer chicken to clean platter and tent loosely with foil. Whisk sour cream and egg yolk together in medium bowl. Whisking constantly, slowly stir 1/2 cup sauce into sour cream mixture (tempering). Stirring constantly, slowly pour sour cream mixture into simmering sauce. Stir in lemon juice and parsley and return to simmer. Season to taste with salt and pepper. Pour sauce over chicken and serve.