01 - Heat olive oil and butter in a large deep skillet or Dutch oven over medium heat until butter melts and begins to sizzle.
02 - Add diced onions, carrots, and celery to the hot pan. Sauté for 5-6 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 brown the garlic.
04 - Sprinkle flour evenly over the vegetables while stirring constantly. Cook for 1-2 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 dried thyme, sage, salt, and black pepper. Bring the mixture to a gentle simmer and cook for approximately 5 minutes, stirring frequently, until the sauce thickens enough to coat the back of a spoon.
07 - Add uncooked gnocchi, shredded chicken, and frozen peas to the simmering sauce. Stir gently to combine, ensuring the gnocchi are submerged in the liquid.
08 - Cover the pot and reduce heat to maintain a gentle simmer. Cook for 10-12 minutes, stirring occasionally to prevent sticking, until gnocchi are tender and cooked through, and the sauce has reached a creamy consistency.
09 - Remove from heat. Stir in grated Parmesan cheese if using, allowing the residual heat to melt and incorporate the cheese into the sauce.
10 - Garnish with chopped fresh parsley and serve immediately while hot.