Combine powdered sugar, butter, and orange zest in bowl of a stand mixer fitted with the paddle attachment. Starting on low speed and gradually increasing speed to high, beat until light and fluffy, about 3 minutes, stopping to scrape down sides of bowl as needed. Reduce speed to low. Add egg, poppy seeds, cardamom, and orange juice, and beat until thoroughly blended, about 1 minute. Gradually add flour and baking soda, beating until incorporated, 30 seconds to 1 minute, stopping to scrape down sides of bowl as needed. Chill, uncovered, 1 hour.

Preheat oven to 350°F with oven racks in middle and lower third of oven. Line 2 rimmed baking sheets with parchment paper, and lightly coat with baking spray.

Using a 1-tablespoon measuring spoon or small ice cream scoop, scoop dough, and shape into 24 balls. Arrange balls 2 inches apart on prepared baking sheets.

Bake in preheated oven until edges of cookies are golden brown and middles are just set, 12 to 15 minutes. Transfer cookies to a wire rack, and let cool completely, about 15 minutes (cookies will continue to crisp as they cool).