Petite Blanquette de Poulet a l'Estragon (Tarragon Chicken)

Pierce whole clove into onion; place into a large soup pot. Add water, white wine, celery, garlic, thyme, parsley, salt, and black pepper; bring to a boil over medium heat. Add chicken pieces and carrots, cover, and simmer for 20 minutes. Transfer chicken pieces to a bowl; strain stock. Reserve about 2 cups stock; discard vegetables and herbs.

Sprinkle chicken pieces with flour. Melt butter in a large skillet over medium heat. Add chicken; cook until golden brown, about 5 minutes per side. Transfer chicken to a plate; set aside. Add mushrooms to the skillet; cook, stirring occasionally, until just starting to brown, about 10 minutes.

Return chicken to the skillet; pour in enough reserved stock to barely cover chicken and mushrooms (about 2 cups). Cover skillet; simmer 20 minutes. Transfer chicken and mushrooms to a serving dish. Boil remaining liquid until reduced by half, stirring constantly, about 10 minutes.

Whisk cream, lemon juice, and egg yolk together in a bowl; remove skillet from the heat. Gradually whisk egg yolk mixture into reduced stock until sauce thickens; whisk in tarragon. Serve sauce over chicken and mushrooms.