Poach the Chicken: Combine chicken broth, thyme, and bay leaf in a large pot. Bring to a gentle boil. Add chicken breasts, reduce heat, and poach for 15–20 minutes or until fully cooked. Remove chicken, let cool slightly, and shred or cut into bite-sized pieces. Strain and reserve the broth.
Cook the Vegetables: Melt 1 tablespoon butter in the same pot over medium heat. Add leek, carrots, and mushrooms. Sauté for 8–10 minutes, stirring occasionally, until tender.
Make the Sauce: Push vegetables to one side. Melt remaining 2 tablespoons butter in the cleared space. Whisk in the flour to form a roux, cooking for 2 minutes. Gradually add the reserved chicken broth while whisking until smooth. Stir in heavy cream. Cook for 2–3 minutes until thickened.
Combine and Finish: Stir in frozen peas, add lemon juice, salt, and pepper to taste. Return chicken to the pot, stirring gently to coat. Simmer for 2-3 minutes until heated through and peas, crisp-tender.
Serve and Garnish: Serve over rice, potatoes, pasta, or in pastry shells. Garnish with fresh parsley.
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