Line a baking sheet with a silicone baking mat or parchment paper. Set aside.
In a medium mixing bowl, whisk together the dry ingredients: flour, cream of tartar, baking soda, and salt. Set aside.
In the bowl of a stand mixer, add the butter, coconut oil, and 1½ cups sugar. Mix until light and fluffy. Add the eggs and the orange zest, mixing until combined.
Gradually add the flour mixture to the wet ingredients, mixing until combined and a dough forms. At this point, refrigerate the dough for 30 minutes. This will help the cookies maintain their “pillowy” status once baked.
A few minutes before the dough comes out of the refrigerator, preheat your oven to 400 degrees.
In a small bowl, combine the cardamom and the ¼ cup sugar.
Using a 1½ tablespoon cookie scoop, form dough balls and roll them in the cardamom and sugar mixture. Place on the prepared cookie sheet, 2 inches apart. Very slightly pat the cookie down. Bake for 8 – 10 minutes. Cool on the baking sheet for a few minutes before removing to a wire rack to cool completely.
Store baked cookies in an airtight container for about a week. They can be frozen for up to 3 months.