I found a recipe for "glass carrots" or carrots glace. I thought corn syrup might be necessary, or a very strong sugar syrup:
12 1/2 pounds carrots 1 1/2 cups boiling water
4 cups corn syrup 1 cup margarine
Wash carrots, and scrape or peel very thinly. Boil in salted water until nearly done, or cook in steamer. Cut in half-inch slices, or cut in quarters lengthwise, and each quarter in two or more pieces, according to length. They may be cut before cooking, if preferred. Put into agate pans to depth of about two inches. Add syrup and margarine to water, with one teaspoon salt; dip over the carrots, and bake forty-five minutes or longer, basting with remainder of mixture.