Bring a large pot of salted water to a boil. Cook the pasta according to the package directions until al dente. Drain and set aside.

While the pasta cooks, melt 1 tablespoon of butter in a large skillet or Dutch oven over medium-high heat.

Add the chicken pieces to the skillet. Season with salt and pepper. Cook until the chicken is browned and cooked through, about 5-7 minutes. Remove the chicken from the pan and set it aside.

In the same skillet, melt the remaining 3 tablespoons of butter. Add the diced onion and cook for 3-4 minutes until softened. Stir in the minced garlic and cook for another minute until fragrant.

Sprinkle the flour over the onions and garlic. Stir constantly for about 1-2 minutes to cook out the raw flour taste.

Slowly pour in the chicken broth while whisking constantly to prevent lumps. Add the milk (or cream), dried thyme, and dried parsley.

Bring the sauce to a gentle simmer. Let it cook for 3-5 minutes until it begins to thicken.

Stir in the frozen mixed vegetables and the cooked chicken. Let them simmer in the sauce for 2-3 minutes until the vegetables are tender and heated through.

Add the cooked pasta to the skillet. Toss everything together until the pasta is thoroughly coated in the creamy sauce. If the sauce is too thick, add a splash of pasta water or broth.

Taste and add more salt or pepper if needed. Garnish with fresh parsley and serve immediately.