In a large mixing bowl, using an electric mixer on medium speed, beat the softened butter until smooth and creamy. Gradually add in the brown sugar and orange zest, mixing until just combined.
Beat in one large egg while scraping down the sides of the bowl. Next, add in the molasses and vanilla extract, continuing to beat until fully incorporated.
Carefully sprinkle the all-purpose flour, baking soda, salt, and ground cardamom over the surface of your dough mixture. Using your mixer on low speed, mix just until combined.
Cover your dough with plastic wrap or transfer it to an airtight container. Refrigerate for at least two hours.
Preheat your oven to 350-degrees Fahrenheit. Scoop out large chunks of dough, roll them lightly in your hands to form balls, then roll each ball in granulated sugar before placing them on the prepared baking sheet. Bake for 11-13 minutes or until just set around the edges.
Allow your orange cardamom cookies to cool slightly on the baking sheet before transferring them to a wire rack to cool completely.