Heat the oil in a small pan and add the garlic and spices. Cook for a couple of minutes, stirring.
Add the sliced carrot and cook for a couple of minutes more, stirring often.
Add the water or apple juice, cook for another 2 minutes, then lower the heat until the mixture is barely simmering. Cover and cook gently until the carrots are tender (5 to 8 minutes). Check occasionally to make sure the pan is not too dry – if it is, add a little more apple juice.