1Slice the chicken breasts in half horizontally to make 8 thin cutlets. Season with salt and pepper and dredge in flour. Heat the butter in a large skillet over high heat. Add the chicken in batches and cook until browned and cooked through, 3 to 4 minutes per side. transfer to a plate.
2Add the onion, thyme, and 1/2 teaspoon salt to skillet. Cook until onion is golden, about 5 minutes. Add the chicken broth and cook until slightly reduced, 3 to 4 minutes. Reduce the heat to medium low.
3Meanwhile, mix egg yolks, pickles, pickle juice, scallions, and parsley into a bowl. Stir into the broth and cook, stirring, Until sauce begans to thicken, about 1 minute. Add chicken to the skillet and cook until the sauce thickens and the chicken is heated through, about 5 minutes (do not boil). Serve with bread and pickled beets, if desired.