01 - Heat olive oil and butter in a large deep skillet or Dutch oven over medium heat. Add onions, carrots, and celery. Sauté for 5-6 minutes until vegetables are soft.
02 - Stir in garlic and cook for 30 seconds until fragrant.
03 - Sprinkle flour over the vegetables, stirring constantly, and cook for 1-2 minutes to form a roux.
04 - Gradually whisk in the chicken broth and milk or half-and-half, stirring well to avoid lumps. Add thyme, sage, salt, and pepper. Bring to a gentle simmer until sauce thickens, about 5 minutes.
05 - Add the uncooked gnocchi, chicken, and peas. Stir gently to combine and ensure the gnocchi are submerged. Cover and simmer for 10-12 minutes, stirring occasionally, until gnocchi are cooked and sauce is creamy.
06 - Remove from heat. Stir in Parmesan if using. Garnish with fresh parsley before serving.