2 cups unsalted chicken stock 1/2 carrot, cut into 1-inch pieces 1/2 celery stalk, cut into 1-inch pieces 1/4 onion, halved 1 bay leaf 1 garlic clove, crushed 4 (6oz) skinless, boneless chicken breast halves 1/2 teaspoon kosher salt, divided 1/2 teaspoon black pepper, divided 3 tablespoons all-purpose flour 2 tablespoons olive oil, divided 2 teaspoons butter, divided 1 cup quartered mushrooms 1/2 cup frozen pearl onions 1 tablespoon water 2 1/2 teaspoons cornstarch 1 tablespoon chopped fresh tarragon

Place first 6 ingredients in a saucepan; bring to a boil. Cook 6 minutes or until reudced to 1 1/4 cups. Remove solids with a slotted spoon; discard.
Cut chicken breast halves in half horizontally to form 8 cutlets. Sprinkle evenly with 1/4 teaspoon salt and 1/4 teaspoon pepper. Place flour in a shallow dish; dredge chicken in flour. Heat a large skillet over medium-high heat. Add 1 tablespoon oil and 1 teaspoon butter to pan; swirl until butter melts. Add 4 cutlets to pan; cook 2 minutes on each side or until golden. Remove from pan; keep warm. Repeat procedure with reamining 1 tablespoon oil, 1 teaspoon butter, and 4 cutlets.
Return skillet to medium-high heat. Add mushrooms and onions; cook 5 minutes or until browned, stirring occasionally. Add stock mixture; bring to a boil, scraping pan to loosen browned bits. Combine 1 tablespoon water and cornstarch in a small bowl. Stir cornstarch mixture into stock mixture; cook 1 minute or until sauce thickens. Stir in remaining 1/4 teaspoon salt, remaining 1/4 teaspoon pepper, and tarragon. Spoon sauce over chicken.