In large bowl, with mixer at low speed, beat sugar and eggs until blended. Increase speed to high; beat until creamy. Reduce speed to low; add flour, grated orange peel, cinnamon, allspice, baking powder, lemon extract, and cloves and beat until well combined, occasionally scraping bowl with rubber spatula. With lightly floured hands, shape dough into 4 balls; flatten each slightly. Wrap each in plastic wrap and freeze 1 hour or refrigerate overnight. (Dough will be very sticky even after chilling.)
Preheat oven to 400 degrees F. Grease large cookie sheet. On well-floured surface, with floured rolling pin, roll 1 piece of dough into 10" by 6" rectangle, keeping remaining dough in refrigerator. With floured pastry wheel or sharp knife, cut dough lengthwise into 6 strips, then cut each strip crosswise into 10 pieces. Place cookies, about 1/2 inch apart, on cookie sheet.