Prep the chicken: If using raw chicken, pat it dry and season with salt and pepper.
If using cooked chicken, shred or dice it and set aside.
Sauté the aromatics: In a large pot or deep skillet, heat olive oil and 1 tablespoon of butter over medium heat. Add onion and carrots with a pinch of salt. Cook 4–5 minutes until softened.
Stir in garlic and cook 30 seconds until fragrant.
Brown the chicken (if raw): Push the veggies to the side, add the chicken pieces, and cook 3–4 minutes, stirring, until lightly browned. It doesn’t need to be cooked through yet.
Make a quick roux: Add remaining 1 tablespoon butter to the pot. Sprinkle in flour and stir to coat the chicken and vegetables.
Cook 1 minute to remove the raw flour taste.
Add the broth: Slowly pour in the chicken broth while stirring to avoid lumps. Add thyme, bay leaf, and Dijon. Bring to a gentle boil.
Cook the noodles: Add egg noodles.
Reduce heat to a brisk simmer and cook according to package directions minus 1 minute, stirring occasionally so they don’t stick. If using cooked chicken, stir it in now to warm through.
Stir in cream: Remove the bay leaf. Pour in the cream (or half-and-half).
Simmer 2–3 minutes, stirring, until the sauce thickens and coats the noodles. If it’s too thick, splash in more broth or a bit of milk. If too thin, simmer another minute.
Finish with peas and seasoning: Stir in the frozen peas and Parmesan, if using.
Cook 1–2 minutes until peas are bright and hot. Taste and adjust with salt and pepper.
Serve: Turn off heat and let it sit 2 minutes to settle. Sprinkle with fresh parsley.
Serve warm, with extra black pepper on top.