In a large deep skillet or sauté pan, melt the butter over medium heat. Add the diced onion and cook until softened, about 3–4 minutes. Stir in the minced garlic and cook for another 30 seconds until fragrant.
Stir in the frozen mixed vegetables and cook for 2–3 minutes. Add the cream of chicken soup, chicken broth, milk, thyme, salt, and pepper. Stir until well combined and bring to a simmer.
Stir in the uncooked egg noodles, making sure they are mostly submerged in the liquid. Reduce the heat to medium-low, cover the skillet, and cook for 10–12 minutes, stirring occasionally, until the noodles are tender and the sauce has thickened. If needed, add a splash more broth or milk.
Add the shredded cooked chicken to the skillet and stir to combine. Let it heat through for 2–3 minutes. If using cheese, stir it in now for extra richness. Taste and adjust seasoning if needed.
Sprinkle with chopped parsley before serving. Dish up into bowls and enjoy warm.