Beat butter in a large mixing bowl for 1 minute. Add sugar and beat with butter until light and fluffy. Add egg and beat for another minute. Beat in orange juice just until combined.
In a separate bowl, whisk together the flour, baking powder and salt. Add to the mixing bowl in two portions, beating just until combined after each addition.
Divide dough in half. Beat the grated orange peel into half the dough.
In a small bowl, stir together the cocoa powder and oil until well combined. Beat into the remaining half of the dough.
Form both halves of the dough into equally-sized logs. Wrap each in plastic wrap and refrigerate at least one hour.
Cut each well-chilled log in half lengthwise. Then cut each half lengthwise in half again.
The finished dough can be refrigerated for several days, so you can make the dough whenever you have time and finish up at a later date. You can also freeze the dough. I recommend slicing the assembled logs and then freezing. That way you can just transfer the slices from the freezer to a baking sheet and just increase the bake time by a minute or two.