This looks close -- and the only one I had by this name. No glaze, though. Hope it is close to what you remember.

Molasses "Cry Baby" Cookies

1 c. molasses
1 c. sugar
1 c. margarine or butter
1 egg
1/2 c. boiling coffee
1 heaping teaspoon baking soda
1 t. cinnamon
4-1/2 c. sifted flour
1 t. vanilla

Cream together sugar, margarine and egg. Add molasses. Dissolve soda in boiling coffee. Add immediately to mixture alternately with flour. Add cinnamon and vanilla. Drop by spoonfuls onto greased cookie sheet. Bake 10 minutes at 375.