Cook pasta in salted boiling water until just under al dente, then drain and set aside.
Melt butter, cook onion 4–5 minutes until soft, then add garlic and cook briefly until fragrant.
Sprinkle in flour and stir 1–2 minutes to form a smooth roux.
Slowly whisk in chicken broth and milk, cooking until thick and creamy.
Add thyme, salt, pepper, and nutmeg, then simmer a few minutes.
Stir in shredded chicken and frozen vegetables, cooking 3–5 minutes until heated through.
Add cooked pasta and mix well to coat with the sauce.
Stir in cheddar cheese until melted and creamy.
Optional: transfer to a baking dish, top with cheese, and bake or broil until lightly golden.
Let cool slightly, garnish with parsley, and serve warm.