Cook pasta in salted water until al dente. Drain and set aside.
Melt butter in a large skillet over medium heat. Add onion and cook until soft. Add garlic and cook 30 seconds.
Sprinkle flour over the vegetables and stir well. Cook for 1 minute.
Slowly pour in chicken broth while stirring until smooth. Add milk and simmer until thickened.
Stir in chicken, mixed vegetables, salt, pepper, and thyme. Cook until heated through.
Add cooked pasta and toss until fully coated in the sauce.
Taste and adjust seasoning. Serve warm, garnished with parsley if desired.