Preheat oven to 350 degrees. Beat sugar, oil, orange peel, vanilla and eggs in large bowl. Stir in remaining ingredients.
Place dough on lightly floured surface. Knead until smooth. Shape half of dough at a time into 10 x 3 inch rectangle on ungreased cookie sheet.
Bake 25 to 30 minutes or until toothpick inserted in center comes out clean. Cool on cookie sheet 15 minutes.
Cut rectangles crosswise into 1/2 inch slices. Place slices, cut sides down, on cookie sheet.
Bake about 15 minutes, turning once, until crisp and light brown. Immediately remove from cookie sheet to wire rack; cool.
Makes about 3 dozen cookies. Store in an air-tight container for up to 4 weeks.