01 - Heat olive oil and butter in a large deep skillet or Dutch oven over medium heat until butter melts and begins to shimmer.
02 - Add diced onions, carrots, and celery to the pot. Sauté 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.
04 - Sprinkle flour evenly over the vegetables, stirring constantly to coat. Cook for 1–2 minutes to eliminate raw flour taste and form a thick paste.
05 - Gradually whisk in chicken broth and milk or half-and-half, stirring continuously to prevent lumps from forming.
06 - Add dried thyme, sage, salt, and black pepper. Bring to a gentle simmer and cook for approximately 5 minutes until sauce thickens enough to coat the back of a spoon.
07 - Stir in uncooked gnocchi, cooked chicken, and frozen peas. Ensure gnocchi are fully submerged in the liquid for even cooking.
08 - Cover and simmer for 10–12 minutes, stirring occasionally to prevent sticking, until gnocchi are tender and float to the surface.
09 - Remove from heat and stir in Parmesan cheese if using. Garnish with chopped fresh parsley before serving hot.