Combine the carrots, water, and salt in a medium saucepan. Bring to a boil and simmer uncovered 10 minutes over medium heat.
Add the sugar, honey, cranberries, and vegetable oil to the pan. Cook uncovered over medium-low heat, stirring occasionally, until carrots are very tender and the liquid is absorbed, about 10 minutes.
Watch so the mixture does not burn. Serve hot or at room temperature.