01 - Heat olive oil and butter in a large deep skillet or Dutch oven over medium heat until butter melts and mixture shimmers.
02 - Add onions, carrots, and celery. Sauté for 5–6 minutes until vegetables soften and onions become translucent.
03 - Stir in garlic and cook for 30 seconds until fragrant, being careful not to burn.
04 - Sprinkle flour over vegetables, stirring constantly. Cook for 1–2 minutes to form a roux and eliminate raw flour taste.
05 - Gradually whisk in chicken broth and milk, stirring well to prevent lumps from forming.
06 - Add thyme, sage, salt, and pepper. Bring to a gentle simmer and cook for 5 minutes until sauce coats the back of a spoon.
07 - Stir in uncooked gnocchi, cooked chicken, and frozen peas. Ensure gnocchi are fully submerged in the liquid.
08 - Cover and simmer for 10–12 minutes, stirring occasionally, until gnocchi float and are tender throughout.
09 - Remove from heat. Stir in Parmesan if using. Garnish with fresh parsley before serving hot.