Preheat the oven to 375°F.
In 12-inch, oven-safe skillet over medium heat, melt the butter.
Add carrots, onion, and celery. Cook, stirring occasionally for 6-8 minutes, or until the vegetables are slightly softened.
Add garlic, thyme, salt, and pepper. Cook for 1 minute.
Sprinkle the flour over the vegetable mixture; stir until combined.
While gently stirring, slowly pour in the turkey stock and milk. Bring the sauce to a simmer, and allow it to simmer for 10 minutes.
Remove from heat and add the turkey and noodles. Stir everything together, gently pressing the noodles down, making sure most of them are covered by the liquid. Top with shredded cheese.
Bake for 30-35 minutes, or until the noodles are cooked and the cheese is hot and bubbling.
Garnish with parsley and serve.