Warm the pan: Set a large skillet over medium heat.
Add olive oil or butter and let it melt and shimmer.
Sauté the aromatics: Add onion, carrots, and celery. Cook, stirring, until the onions turn translucent and the carrots start to soften, about 5–7 minutes. Add mushrooms, if using, and cook 3 minutes more.
Add garlic and spices: Stir in garlic, thyme, smoked paprika, salt, and pepper.
Cook 30 seconds until fragrant.
Make a quick roux: Sprinkle flour over the vegetables. Stir well to coat. Cook 1 minute to remove the raw flour taste.
Build the sauce: Slowly pour in chicken broth while stirring to prevent lumps.
Bring to a gentle simmer; the mixture will thicken. Stir in milk or half-and-half and the Dijon mustard. Adjust heat to keep it at a light bubble.
Add chicken and peas: Fold in shredded rotisserie chicken and frozen peas.
Simmer 3–5 minutes, until the chicken is heated through and the sauce is creamy. If it’s too thick, splash in more broth or milk.
Taste and finish: Taste and season with more salt and pepper if needed. Stir in fresh parsley or chives.
Squeeze a little lemon over the top for brightness, if you like.
Serve: Spoon the creamy chicken and vegetables over rice, buttered noodles, or mashed potatoes, or serve with crusty bread to soak up the sauce.