Originally, these came with marshmallow frosting. Cream cheese frosting didn’t generally show up on carrot cakes until around the 1950s.
Here’s a version from 1914’s From The Neighborhood Cook Book, compiled by The Council Of Jewish Women:
One-half pound sugar, one-half pound almonds, blanched and chopped, one-half pound carrots, boiled only till they can be grated, juice and grated rind of one lemon, four eggs. Cream the yolks and sugar; whites beaten to snow, added last; add three or four bitter almonds; beat for one-half hour before adding whites of eggs. Butter spring form and sprinkle with grated zwieback. Bake in a moderate oven one and one-quarter hours, till loosened from pan.
From a box sold in River Forest, Illinois.
3 c. sifted flour
2 c. sugar
1 tsp. salt
3 tsp. baking powder
2 tsp. cinnamon
2 c. raw carrot
1-1/4 c. melted margarine
4 eggs, beaten
1/2 c. chopped nuts (if desired)
Sift flour once, measure and re-sift into mixing bowl with sugar, salt, baking powder, soda, and cinnamon. Add carrots, margarine, and eggs and beat at medium speed until batter is smooth and well blended. Fold in nuts.
Bake in greased 10″ tube pan in 350 deg. oven 1 hour or until done.