In a deeper pot, heat oil over high. Add onion, garlic, and carrots. Stir and simmer 1-2 minutes. Add peppers. Lower temperature to medium and continue simmering for 8-10 minutes.
Add chicken, seasonings and one cup of chicken broth to the pot. Simmer for 15-20 minutes, occasionally stirring.
(If making dumplings) Whisk egg and flour together until integrated and set aside (you can leave it in the fridge if you like).
Add potatoes, tomato sauce and parsley, and the remaining chicken broth. Raise the temperature and bring stew to a boil, then lower to medium and continue cooking for 20-30 minutes.
Add dumplings by taking a little bit of the mixture with a teaspoon and lightly flicking it into the stew. (Dip the empty spoon into the stew after every fourth or fifth dumpling to keep it hot and prevent from sticking.)
Cook for 3-5 additional minutes.
Adding both potatoes and dumplings is a choice. If you want a thinner stew use one or the other.Dumplings can be made in several different ways (look at the text above). The ones chosen for the recipe are easiest to make and super tasty.