In the bowl of a stand mixer fitted with the paddle attachment or in a large mixing bowl, add the sugar, orange oil, orange juice, and eggs. Beat on medium speed until thick and creamy, about 3 minutes.
In a separate bowl whisk together the flour and remaining dry ingredients.
Add the dry ingredients to the wet ingredients in three additions beating in between additions until no dry spots remain.
Pipe the cookie dough using a pastry bag fitted with a star shaped pastry, portioning approximately two teaspoons of dough per cookie, onto a parchment lined cookie sheet pan. Alternatively, use two spoons to drop batter onto the cookie sheet. Bake in the center of the oven for 10 minutes.
Increase the heat to 425 F and bake for an additional 2 minutes to aid in creating a golden brown exterior. Remove the cookies to a rack to cool. Repeat with the remainder of the dough. When fully cooled, dust with powdered sugar. Yields about 48 cookies