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 to the pan. Sauté for 5-6 minutes, stirring occasionally, until vegetables begin to soften and onions turn translucent.
03 - Stir in minced garlic and cook for 30 seconds until fragrant, being careful not to brown it.
04 - Sprinkle flour evenly over the vegetables, stirring constantly to coat. Cook for 1-2 minutes to form a roux, eliminating raw flour taste.
05 - Gradually whisk in chicken broth and milk (or half-and-half), stirring continuously to prevent lumps and create a smooth base.
06 - Add thyme, sage, salt, and pepper. Bring mixture to a gentle simmer and cook for about 5 minutes, stirring occasionally, until sauce thickens enough to coat the back of a spoon.
07 - Stir in uncooked gnocchi, shredded chicken, and frozen peas. Ensure gnocchi are submerged in the liquid for even cooking.
08 - Cover and reduce heat to maintain a gentle simmer. Cook for 10-12 minutes, stirring occasionally to prevent sticking, until gnocchi are tender and sauce is creamy and thickened.
09 - Remove from heat and stir in Parmesan if using. Garnish individual portions with chopped fresh parsley before serving hot.