Cook the cavatappi pasta according to the package directions. Strain the pasta and set it aside.
Meanwhile, heat the butter in a Dutch oven or large pot over medium heat. Add the diced celery and onion. Cook them until they're softened, for about 9 to 10 minutes, stirring occasionally.
Stir in the mixed vegetables, garlic, thyme, salt and pepper. Cook the mixture until the vegetables are soft, about four to five minutes.
Stir in the flour and cook it until it's lightly browned, about two to three minutes, stirring frequently.
Stir in the chicken broth and heavy cream. Increase the heat to medium-high and bring the liquid to a simmer. Reduce the heat to medium-low. Cook until the mixture is thickened, five to seven minutes, stirring occasionally.
Stir in the cooked pasta and cooked chicken. Cook them until they're hot, four to five minutes, stirring occasionally. Season the pasta with extra salt and pepper to taste.
Spoon the chicken potpie pasta into serving bowls. Top each dish with a sprinkle of optional chopped, fresh parsley and a freshly baked biscuit, if desired.
