In a medium pot, combine cubed chicken and vegetables. Add water to cover and boil for 12-15 minutes, until chicken is cooked through to 165 F. Remove from heat, and set aside (Don't strain - you'll use the liquid later in the recipe)
In a large pot, cook onions and celery in butter until translucent. Add garlic and saute until fragrant, about 30 seconds more. Stir in flour, salt, pepper, and poultry seasoning to form a paste.
Slowly mix in chicken broth and milk, about 1/2 cup at a time. Stir and bring to boil. Reduce heat to low and simmer for 2-3 minutes or until sauce thickens. Stir in chicken and veggie mixture, along with the liquid. Season to taste with salt and pepper.
Meanwhile, in a separate pot, cook pasta as directed on the packaging. Once cooked, strain and add to soup. Stir and serve!