Preheat oven to 375°F and set out two baking sheets. Do not grease or line them.
In a large bowl, cream together butter and brown sugar until fluffy. Mix in molasses, egg, and vanilla until smooth and creamy.
In another bowl, stir together flour, cinnamon, ginger, cloves, cardamom, and salt.
Stir flour mixture into wet ingredients in batches, mixing well after each addition. Chill dough for 30 minutes.
While dough chills, whisk together the powdered sugar and milk to create a thin icing and set aside.
Fit chosen disc to cookie press and screw into bottom. Fill press barrel with about 1 cup of dough, screw on top, and press trigger until dough reaches the disc.
Set press bottom onto cookie sheet and press trigger to push out a cookie, then lift straight up. The cookie should stick to the pan. (You may need to do a few "primer" cookies to get it ready.) Repeat with remaining dough, leaving about 1 inch between cookies.
Bake cookies for 6-8 minutes, then let cool on the pan for 5 minutes. Dip each cookie into the icing, let the excess drip off, then place on a wire rack to cool completely.
Notes
Chill remaining unshaped dough while cookies bake.
If you can, swap your baking sheets between bakes so that you are not piping onto a hot pan.