Grind almonds very finely in a food processor. Combine ground almonds with flour, baking powder, cinnamon and salt in a large mixing bowl until well blended; set aside.
Beat sugars, oil, eggs, orange peel and vanilla in large bowl with electric mixer for 1 minute, until well combined and pale in color. Add dry ingredients and mix until dough forms.
Divide dough in half and shape into two (2-inch diameter) logs. Wrap logs in parchment or waxed paper and freeze for at least 2 hours or up to 1 month.
Preheat oven to 350°F. Line baking sheets with parchment paper. Cut dough into 1/4-inch thick slices and place 1-inch apart on prepared baking sheets. Bake 8 to 10 minutes or until bottom edges appear light golden brown.
Cool cookies for 1 to 2 minutes on baking sheet and then transfer to cooling rack. Store in closed container for up to 1 week or freeze for up to 2 weeks.
Recipe Suggestion: To garnish, sprinkle cookies with coarse sugar and top with almond slivers; lightly press into the surface just prior to baking.