Heat the olive oil in a large pot or Dutch oven over medium heat. Add the chicken, season with salt and pepper, and cook until lightly browned but not completely cooked through. Transfer to a plate and set aside.
Add the onion, carrots, celery, and garlic to the same pot. Cook for about 5–7 minutes, stirring occasionally, until the onion is soft and the vegetables begin to become tender.
Add the butter and let it melt. Sprinkle the flour over the vegetables and stir continuously for 1–2 minutes.
Slowly pour in the chicken broth and milk while stirring to keep the sauce smooth. Add the thyme, paprika, and Parmesan cheese. Bring to a gentle simmer and cook until the sauce begins to thicken.
Return the chicken to the pot. Add the gnocchi and frozen peas and stir gently to combine.
Cover and simmer for about 5–7 minutes, or until the gnocchi is tender and the chicken is completely cooked through.
Taste and adjust the salt and pepper as needed. If the sauce is too thick, stir in a small splash of broth or milk.
Serve hot with fresh parsley or chives on top.