Chop the carrots into rounds that are no more about 1 cm (1/3 inch) thick....... not too thick and not too thin (now, don't you feel like Goldilocks!).  If you have a mandolin or food processor that does this for you, use it!

Heat the oil in a large frying pan.

Add the whole clove of garlic and the whole rosemary sprigs. Cook for 1-2 minutes.

Add the carrots. Sauté them on medium-high heat for 5 minutes, stirring often.

Add water to cover the carrots.  Wait until it is simmering, and then turn the heat down to medium.

Continue to cook the carrots for approximately 1 hour, gently stirring occasionally.  If the water boils off too quickly, add more.  You should be left with a bit of water in the bottom of the pan at the end of the hour.

Turn the heat up to medium-high again and cook for 20 -25 minutes, until the water has boiled off and the carrots are becoming browned.  Stir often, otherwise the carrots will burn, but stir gently, otherwise they will break apart.