In a dutch oven over medium heat, melt the butter.
Add the celery, carrots, potatoes, onion, and garlic and cook until the onions are soft and translucent, about 7 minutes (sprinkle in a little salt and pepper as it cooks).
Add in the broth, Better Than Bouillon, chicken, tomatoes (and their juices), cayenne pepper, thyme, and poultry seasoning. Bring to a boil, then reduce heat to a simmer, and cover.
Stir the soup occasionally while it cooks. Simmer for 25-30 minutes until the potatoes are tender. Taste and make adjustments to the seasoning if needed.
To serve, add some cooked Ditalini pasta to a bowl and ladle the soup over the pasta (I like to do it this way because if you leave the pasta in the soup it tends to soak up the liquid and get really mushy).