Bring a large pot of salted water to a boil and cook the pasta according to package directions until al dente.
In a large skillet or Dutch oven, melt the butter over medium heat. Add the onion and sauté for 5 minutes until translucent.
Add the garlic and cook for 1 minute until fragrant.
Whisk in the flour and cook for 2 minutes, stirring constantly, to create a roux.
Gradually whisk in the chicken broth and heavy cream. Simmer for 5 minutes until the sauce begins to thicken.
Stir in the shredded chicken, frozen vegetables, thyme, salt, and pepper. Simmer for an additional 5-7 minutes until vegetables are heated through.
Drain the pasta and add it directly to the skillet. Toss until the pasta is thoroughly coated in the sauce.
Garnish with chopped fresh parsley and serve immediately.