Preheat oven to 325°
Stir together first 4 ingredients.
Beat sugar, butter olive oil, and zest at medium speed with an electric mixer until creamy.
Add eggs, 1 at a time, beating well after each addition.
Add flour mixture and cranberries, beating just until blended.
Divide dough into 3 equal portions; shape each into a 12 1/2- x 9-inch slightly flattened log, using lightly floured hands. Place about 2 inches apart on a parchment paper-lined baking sheet.
Bake at 325° for 30 to 35 minutes or until light brown. Transfer to wire racks; cool 15 minutes.
Reduce oven temperature to 300°.
Cut each log into 1/4- to 1/2-inch-thick slices using a serrated knife. Place on 3 parchment paper-lined baking sheets.
Bake at 300° for 30 to 35 minutes or until golden brown.
Cool on baking sheets 10 minutes; transfer cookies, on parchment paper, to wire racks, and cool.