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 heat to back 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 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.
Roll out dough to about 1/4 inch thickness and cut small rectangles. Place in simmering broth, OR, 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 10 minutes for rolled, cut rectangles OR 15-20 minutes for spoonful size, gently turning dumplings until they are floating and fluffy on the outside.