Preheat oven to 350 degrees Fahrenheit (175 degrees Celsius) and line baking sheets with parchment paper.

In a small bowl, whisk together baking soda, ground cardamom, ground cinnamon, and flour.

In a large bowl, cream together sugar and butter with an electric mixer on medium-high speed until light and fluffy.

Add egg to the sugar and butter mixture and beat until thoroughly combined.

Reduce mixer speed to low and gradually add the flour mixture until just combined.

Roll dough into small balls.

Place dough balls on prepared baking sheets, spacing 2 inches apart.

Flatten each dough ball with the bottom of a drinking glass.

Bake for 14 to 16 minutes, or until lightly browned.

Remove from oven and let cool on baking sheets for 2 minutes.

Transfer cookies to a wire rack to cool completely.

For the icing, in a large bowl, beat butter and vanilla extract with an electric mixer on medium-high speed until light and fluffy.

Add milk, ground cardamom, and ground cinnamon to the icing mixture and beat well.

Reduce mixer speed to low and gradually add powdered sugar until desired consistency is reached.

Spread icing on cooled cookies.