01 - Heat olive oil and butter in a large deep skillet or Dutch oven over medium heat.
02 - Add onions, carrots, and celery. Sauté for 5–6 minutes until vegetables are softened and fragrant.
03 - Stir in garlic and cook for 30 seconds until fragrant, being careful not to burn.
04 - Sprinkle flour over the vegetables, stirring constantly. Cook for 1–2 minutes to form a roux and eliminate raw flour taste.
05 - Gradually whisk in the chicken broth and milk or half-and-half, stirring well to prevent lumps from forming.
06 - Add thyme, sage, salt, and pepper. Bring to a gentle simmer and cook for about 5 minutes until sauce thickens enough to coat the back of a spoon.
07 - Add uncooked gnocchi, cooked chicken, and frozen peas. Stir gently to combine, ensuring gnocchi are submerged in the sauce.
08 - Cover and simmer for 10–12 minutes, stirring occasionally to prevent sticking, until gnocchi are tender and sauce has reached a creamy consistency.
09 - Remove from heat. Stir in Parmesan cheese if using. Garnish with fresh chopped parsley and serve hot.