Dredge chicken breasts in flour, dip in milk, then dredge again in bread crumbs.
Saute chicken in butter until browned on all sides. Remove chicken and put to the side.
Saute carrots, celery, onion, and garlic in the same pan used for cooking chicken. When vegetables are tender, stir in thyme, basil and parsley.
Spoon vegetable mixture into 9x13 baking dish saving the liquid for later. Sprinkle chopped peanuts over mixture. Pour chicken broth and white cooking wine over the vegetables and peanuts. Place chicken breast on top and cover pan tightly with foil. Bake at 375° F. for 45 minutes. Uncover and sprinkle with Parmesan cheese. Bake uncovered for 25 minutes. Keep warm.
Place strained juices from vegetable mixture into a small saucepan. Bring juices to a boil. Remove from heat and whisk in yolks and heavy cream. Add salt, pepper, and additonal parsley.
Serve chicken on top of vegetable mixture and top with sauce.