Melt 3 Tbl butter in Dutch oven over Med heat. Add onion and celery and cook until translucent, about 3 minute Stir in tomatoes and their juice, sugar, salt, and pepper. Bring to a simmer and cook until veggies are softened, about 5 minute Remove from heat and stir in 2 Tbl parsley.
Combine remaining parsley, flour, and baking powder in a bowl. Stir in milk, egg, and melted butter until combined and smooth. Return tomato mix to simmer over Med heat.
Using greased Tbl measure, drop heaping Tbl-size dumplings on top of tomato mix, leaving about 1/2-in between dumplings. Cover and cook over low heat until dumplings are firm and cooked through, about 20 minute Take care not to uncover during cooking. Serve.