01 - Warm 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. Cook for 5–6 minutes, stirring occasionally, until vegetables soften and onions become translucent.
03 - Stir in minced garlic and cook for 30 seconds until fragrant, being careful not to burn it.
04 - Sprinkle flour evenly over the vegetables. Stir constantly for 1–2 minutes to cook off the raw flour taste and form a thick paste.
05 - Slowly whisk in chicken broth and milk (or half-and-half), stirring continuously to prevent lumps from forming.
06 - Add thyme, sage, salt, and pepper. Bring mixture to a gentle simmer and cook for about 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 the pan and simmer for 10–12 minutes, stirring occasionally, until gnocchi are tender and sauce has thickened nicely.
09 - Remove from heat. Stir in Parmesan cheese if using. Garnish with chopped fresh parsley and serve hot.