01 - Heat olive oil and butter in a large deep skillet or Dutch oven over medium heat until butter melts.
02 - Add onions, carrots, and celery to the pan. Sauté for 5–6 minutes until vegetables begin to soften and onions become translucent.
03 - Stir in minced garlic and cook for 30 seconds until fragrant, being careful not to burn.
04 - Sprinkle flour evenly 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, stirring continuously to prevent lumps from forming.
06 - Add thyme, sage, salt, and pepper. Bring mixture to a gentle simmer and cook for approximately 5 minutes until sauce thickens enough to coat the back of a spoon.
07 - Add uncooked gnocchi, shredded chicken, and frozen peas to the sauce. Stir gently to combine and ensure gnocchi are fully submerged in the liquid.
08 - Cover the pan and simmer for 10–12 minutes, stirring occasionally to prevent sticking, until gnocchi are tender and cooked through.
09 - Remove from heat. Stir in Parmesan cheese if desired. Garnish with chopped fresh parsley before serving hot.