Place the butter in a big pot over low warmth and soften. Add the carrots, celery, onion, zucchini and garlic to the pot. Stir after which put the lid on the pot and let sweat for half-hour.
Add the rooster breasts, broth, salt and pepper and convey to a boil over excessive warmth. Cut back warmth to medium-low and proceed to simmer till rooster is cooked by way of, about 8 minutes. Utilizing a pair of tongs, take away the rooster and place on a chopping board. Minimize the rooster into bite-size items after which add again to the broth combination.
In a small bowl, whisk collectively the egg yolks and lemon juice. Slowly add 1/2 cup of the recent liquid to the egg yolks whereas whisking continually. Then, slowly add the yolk combination to the soup whereas whisking continually.
Add the parsley, season with further sea salt and pepper if wanted, and serve.