In a large pot or Dutch oven, melt butter over medium-high heat. Add chicken pieces and cook until browned on all sides, approximately 5 minutes.
Add onion, carrots, and celery to the pot. Sauté for 5 minutes until the onion is translucent and vegetables soften.
Stir in minced garlic and cook for 1 minute until fragrant.
Sprinkle flour over the chicken and vegetable mixture. Stir constantly for 2 minutes to incorporate and cook the flour.
Slowly pour in the chicken broth while stirring continuously to ensure a smooth base. Add thyme, salt, and pepper.
Add the dry pasta to the pot, ensuring it is mostly submerged in liquid. Bring the mixture to a boil.
Reduce heat to medium-low, cover, and simmer for 10 to 12 minutes, or until the pasta is al dente. Stir occasionally to prevent the pasta from sticking to the bottom.
Stir in the heavy cream and frozen peas. Continue to cook uncovered for 2 to 3 minutes until the sauce thickens and the peas are warmed through.
Remove from heat and allow the pasta to rest for 5 minutes to thicken the sauce further before serving.