Heat 1 tablespoon olive oil in soup pot over medium high heat. Season chicken with salt and pepper (about 1/2 teaspoon each). Add the chicken and brown on all sides, about 3-4 minutes total. Remove chicken from the pan.
Add second tablespoon of olive oil to the pan. Cook onion, celery, and carrot for two minutes, stirring often. Add the garlic, cook one minute. Add the potato, salt, pepper, and Italian seasoning and cook for another minute.
Stir flour into vegetables and cook one minute then stir in chicken stock. Stir to remove anything stuck to the bottom of the pan. Cover and bring to a boil.
Meanwhile, make the dumplings by stirring all ingredients for the dumplings in a medium sized bowl. Mixture will be thick. Set aside.
Boil soup for about 4-5 minutes then add the chicken back to the pan. Cook until potatoes are fork tender.
Add the peas to the pot and stir.
Drop dumplings into the pot using two spoons. This recipe makes about 6 dumplings, unless you want them smaller or larger.
Cover the pot and cook until the dumplings are cooked, 8-11 minutes. Serve hot.