In a saucepan, place carrots that have been scraped and cut into small cubes. Peel potatoes, cut into cubes and add to carrots. Add butter, onion, sugar, and ginger, and just enough water to cover. Bring to a boil.
When carrots and potatoes are very tender and water has boiled down considerably, mix the cornstarch with a little cold water until smooth, and add some of the carrot water. Add slowly to carrot mixture stirring carefully so as not to mash the tsimis.