Cook the pasta according to the package instructions until al dente. Drain and set aside.
In a large skillet, heat the olive oil over medium heat. Add the diced onion, carrots, and celery. Sauté for about 5-7 minutes, or until the vegetables are tender.
Add the minced garlic and cook for an additional minute, stirring frequently to prevent burning.
Stir in the shredded cooked chicken and frozen peas, mixing well to combine.
Pour in the chicken broth and heavy cream. Add the dried thyme, salt, and black pepper. Mix well and bring to a simmer.
Allow the mixture to simmer for about 5 minutes until slightly thickened.
Add the cooked pasta to the skillet and stir to combine, ensuring all pasta is coated with the creamy mixture.
If using, transfer the mixture to a baking dish and sprinkle the pie crust crumbs or lay the puff pastry on top. Bake in a preheated oven at 375°F (190°C) for about 15-20 minutes or until the top is golden brown.
Remove from the oven and let it cool for a few minutes before serving.