In a stand mixer fitted with the paddle attachment (or using a hand mixer and a large mixing bowl), beat the butter and sugar at medium speed until they're fluffy, about 2 minutes. Beat in the vanilla, orange zest, and orange juice.
Add the flours and salt (you can do this in two rounds to avoid flour flying everywhere as you mix) and mix at low speed till the dough is well combined. It will be soft. Shape it into two disks, wrap it with saran, and transfer to the refrigerator for at least 1 hour to chill.
Preheat your oven to 350F and line two baking sheets with parchment paper.
Flour a clean surface and use a rolling pin to roll the disks of dough to 1/4-inch thickness. Use a cookie cutter to cut the dough into shapes, then transfer them to the baking sheets. Prick each cookie a couple times with a fork. Bake for 8-10 minutes, or until the cookies are firmed up, but not browning (it's OK if they're just barely golden, but they shouldn't get dark at the edges). Transfer the baking sheets to a wire rack to cool for 20 minutes, then transfer the cookies from the sheet to the rack and allow them to cool entirely before enjoying.
*You can substitute 2 cups of unbleached, all-purpose flour.