In large skillet, add first 5 ingredients. Heat to medium, stirring frequently until veggies are tender (about 5 minutes).
Add chicken broth, carrots, and peas and bring to a boil.
Turn down heat to medium and add chicken pieces, salt, and pepper.
Cover and cook on medium heat until carrots are tender (15-20 minutes)
While soup is cooking, prepare dumplings.
In a large mixing bowl, combine flour, baking powder, and salt. Add butter in smallish pieces.
With your hands (or a pastry blender), combine flour mixture and butter until butter is pea sized and mixture is crumbly.
Pour in milk and combine with a wooden spoon until well incorporated, taking care not to over mix.
Drop dumplings by small spoonfuls into simmering broth, adding a dumpling to each empty spot. Keep dropping and lightly stirring to move dumplings around as they cook to make room for more.
Once all dough is added, cook approximately 15-20 minutes, gently turning dumplings until they are floating and fluffy on the outside. Note: They will still be a bit doughy inside while done on the outside.