Peel, wash, and slice carrots into 3/8 inch disks.

Place carrots and butter in a saute pan large enough to hold carrots in a single layer.

Add water to come 1/4 inch up the sides of the carrots.

Cook over medium heat, uncovered, until the water has evaporated.

Add salt and sugar.

Continue cooking, adding 2-3 tablespoons of water as needed, until carrots are well-browned and wrinkled, about 1-1.5 hours.

Reduce the number of pans used if necessary.

When carrots are very tender, add the grated Parmesan cheese.

Turn the carrots over completely once or twice to coat with cheese.

Transfer to a warm platter and serve immediately.