To make the dough, mix together the flour, baking powder, and salt. In a small saucepan, heat the butter and milk until the butter melts. Add the warm milk mixture to the dry ingredients and mix.
In a large pot, bring the broth just to a boil, then lower the heat to medium. Add 1 cup of the carrots.
Form 1/2-inch balls of dough and add them to the pot. Simmer uncovered over medium-low heat for 8 to 10 minutes. The broth will thicken as the dumpling batter breaks down a bit.
Divide the soup into bowls and sprinkle each bowl with the remaining carrots.