Cook the pasta until al dente. While the pasta cooks prep the vegetables and chicken. Once the pasta is cooked, drain it and set aside. Return the pot or pan to the stove and heat the olive oil over medium-high.
Add in the onion, carrots and celery and season with salt and pepper. Sauté the vegetables until they've softened slightly, about 5 minutes. Add in the garlic, peas and fresh herbs and sauté another minute.
Sprinkle the flour over the vegetables and stir it in until it's combined with the vegetables. Slowly pour in the chicken broth, stirring constantly to prevent lumps from forming. Pour in the milk and stir in diced chicken. Cook over medium heat, stirring occasionally, until the sauce has thickened, about 5 minutes.
Add in the pasta and stir together until it is completely coated in the sauce. Turn off the heat and stir in the Greek yogurt. Serve the pasta topped with extra fresh thyme leaves desired.
Notes
Leftover chicken pot pie pasta will keep for 3-4 days in an airtight container in the fridge. I don't recommend freezing it.