Combine oil and 1 cup sugar in a large mixing bowl; beat at medium speed of an electric mixer until well blended. Add egg, and beat well. Gradually stir in molasses.
Sift together flour, soda, salt, ginger, and cinnamon in a medium mixing bowl; gradually add to creamed mixture, stirring well after each addition.
Place remaining sugar in a small mixing bowl; drop dough by teaspoonfuls into sugar, rolling to coat well.
Place balls 3 inches apart on lightly greased cookie sheets. Bake at 350° for 8 to 10 minutes. (Cookies will flatten and crinkle.) Cool slightly on cookie sheets. Remove from cookie sheets, and cool completely on wire racks. Store in airtight containers.