3 tablespoons unsalted butter, melted and slightly cooled
2 medium carrots, thinly sliced
1/2 large head savoy cabbage, large dice (about 6 cups)
Heat oil in a large, shallow pot over medium-high heat. When oil shimmers, add onion, celery, and garlic and season generously with salt and freshly ground black pepper. Cook until onions begin to soften, about 5 minutes. Add broth and chicken and bring to a boil.
Meanwhile, whisk together flour, chives, salt, and baking powder in a large bowl to break up any lumps. Stir in milk and butter until dough just comes together (it will be very thick). When chicken is cooked through (it will be firm and opaque), add carrots and cabbage and reduce heat to medium low. Add additional salt and pepper if necessary.
Drop 1 heaping tablespoon of dough at a time into soup and repeat until all dough has been used. Cover and cook until dumplings are fluffy and cooked through, about 10 minutes.