01 - Heat olive oil and butter in a large deep skillet or Dutch oven over medium heat until butter melts and begins to foam.
02 - Add onions, carrots, and celery to the pan. Sauté for 5 to 6 minutes, stirring occasionally, until vegetables are softened and onions are 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 while stirring constantly. Cook for 1 to 2 minutes to form a roux and eliminate raw flour taste.
05 - Gradually 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 approximately 5 minutes, stirring frequently, 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 the pan and simmer for 10 to 12 minutes, stirring occasionally to prevent sticking, until gnocchi are tender and sauce has thickened further.
09 - Remove from heat. Stir in Parmesan cheese if using, allowing it to melt into the sauce. Garnish with chopped fresh parsley before serving hot.