Preheat your oven to 350°F (175°C). Line baking sheets with parchment paper.
In a medium bowl, whisk together the flour, sugar, cardamom, and salt.
Using a hand or stand mixer, beat the softened butter and vanilla extract until creamy.
Gradually add the dry ingredients and mix until the dough comes together.
Roll the dough into 1-inch balls and place them on the prepared baking sheets about 2 inches apart.
Flatten each ball gently with the bottom of a glass or your fingers.
Bake for 10-12 minutes, or until the edges are lightly golden.
Allow the cookies to cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely.
In a small bowl, whisk together the powdered sugar, orange juice, and orange zest until smooth to make the glaze. (Adjust consistency as needed.)
Drizzle the glaze over the cooled cookies and allow it to set for 20 minutes before serving.