1. Peel and cut the carrots into chunks. Peel and crush the garlic. Wash the vegetables. In a Dutch oven, place the carrots, leek greens, celery, bouquet garni, peppercorns, coriander seeds, garlic, onion, coarse salt, and finally the chicken pieces. Cover with water, bring to a boil over high heat, skimming off any foam as needed. Simmer for 45 minutes.
2. Meanwhile, trim the stems of the mushrooms, then brush and cut them into quarters. Peel the pearl onions. In a sauté pan, melt 45 g of butter and sauté the mushrooms and onions over low heat for 5 minutes, then set aside in a small bowl.
3. In a bowl, mix the cream with the egg yolk and nutmeg.
4. In the same sauté pan, melt 65 g of butter, then add the flour, whisk to combine, and gradually add 1 liter of the chicken cooking liquid, incorporating it ladle by ladle. Finally, stir in the cream.
5. Reduce the heat and add the chicken pieces, carrots, mushrooms, and pearl onions to the sauce, continue cooking for 10 minutes over low heat. Season with salt and freshly ground pepper if needed, and sprinkle with coriander.