In your mixer at low speed, combine flour, sugar, cardamom, and salt
Add butter piece by piece and mix until dough looks like wet sand ~2 minutes
Add egg and vanilla extract and beat until dough starts to come together (you're looking for a couple big hunks of dough here) ~30s-1m
Turn out onto the counter and knead only until it comes together into a ball of dough
Divide in two, form into balls and flatten into disks.
Wrap each disk in plastic wrap (cling film) and chill in the refrigerator at least 3-4 hours and up to a day or two (if chilling longer, you may want to thaw slightly before rolling)
Preheat oven to 350F/180C/160F position the rack in the middle rack
Cut parchment to size for your baking sheets.
Working with one disk at a time, leaving the 2nd in the fridge to chill, roll the dough out between two pieces of parchment or wax paper to ¼ inch thick. Cut your cookies and carefully transfer them to the baking parchment spacing them about 1 inch apart.
Re-roll the scraps and cut out cookies for as long as you're happy to. If it gets too soft, roll it to ¼ inch thick and chill in the fridge for ~10 minutes before continuing to work. (Not a bad idea to chill the raw cookies on the cookie sheet while you're at it)
Now's the time to decorate - if you decorate your cookies pre-baking. Sprinkle the cookies with princess sugar, coloured sugar, egg wash, sprinkles, your choice. Bake, 1 sheet at a time 6-9 minutes, rotating the sheet after about 4 minutes. When the cookies are done they'll just start to take a little color on the top and maybe appear a little darker on the edges.
Cool on the cookie sheet for 3-5 minutes, then transfer them to a wire rack to finish cooling.
If you're more a "decorate after" type - i.e. you use glaze - do so once the cookies have cooled completely.