Melt the butter in a large pot over medium heat. Add the carrots, celery, and leek and cook, stirring occasionally, until tender, 6 to 8 minutes.
Sprinkle with ½ cup of the flour and cook, stirring, for 1 minute (do not let it darken).
Stir in the broth, wine, ½ teaspoon salt, and ¼ teaspoon pepper and bring to a boil. Add the chicken and reduce to a simmer.
Meanwhile, in a medium bowl, whisk together the remaining 1 cup of flour, baking soda, and ¼ teaspoon salt. Stir in the sour cream and egg.
Drop full tablespoons of the dough into the stew and cook, covered, until the dumplings are plump and cooked through, 15 to 17 minutes.
Sprinkle the soup with the dill before serving.