Cut a 1-inch chunk off one end of a carrot at an angle. Roll the carrot a quarter turn and cut another 1-inch chunk at an angle. Continue rolling and cutting all of the carrots into 1-inch chunks. Combine the carrots and orange juice in a large saucepan. Add enough water to just cover the carrots. Add the butter and 1/4 teaspoon each salt and pepper.
Bring to a boil, and then reduce the heat to maintain a steady simmer. Cook, stirring occasionally, until the carrots are tender and the liquid has reduced to a glaze, about 20 minutes. Top with the dill and serve.