Pat the chicken dry, and lightly pound the chicken breast to an even layer using a meat mallet (or a metal ladle). Season both sides with salt and pepper.
Heat a medium size skillet over medium high heat. Add the butter and olive oil, and cook the chicken on 4 minutes per side. Remove chicken from skillet and transfer to a plate.
Add the mushrooms, onions and wine to the skillet and cook for 8-10 minutes, until the liquid has evaporated and the mushrooms are browned, stirring occasionally. Add the garlic and flour, and stir for 1 minute. Add the chicken broth to the mushroom mixture, scraping up the browned bits. Add the chicken back to the skillet, cover with a lid and cook until the chicken is cooked thru to 165 degrees, about 5-10 minutes. Remove the chicken from the pan and tent with foil.
In a medium size mixing bowl, whisk together the sour cream and egg yolk. Add in a ladle full of the mushroom mixture to the sour cream sauce, and whisk to temper. Then add the sour cream mixture to the pan and stir to combine. Add lemon zest, lemon juice and parsley. Taste for salt and pepper. Pour the mushroom mixture over the chicken.