Bring chicken stock to a boil in a large saucepan. Add carrots; season with salt. Reduce heat and simmer until carrots are tender, 5–7 minutes. Remove from heat, add reserved breast meat, and cover. Set soup aside.
Meanwhile, bring a large pot of well-salted water to a boil. Scoop out 2-tablespoonful portions of matzo ball mixture and, using wet hands, gently roll into balls.
Add matzo balls to water and reduce heat so water is at a gentle simmer (too much bouncing around will break them up). Cover pot and cook matzo balls until cooked through and starting to sink, 20–25 minutes.
DO AHEAD: Using a slotted spoon, transfer matzo balls to bowls. Ladle soup over, top with dill, and season with pepper.