How to make stiff mashed potatoes?
The second easiest way to get stiff, but still edible mashed potatoes is to bake the potatoes whole, then put them through a ricer.

The easiest way is to use potato flakes ... and then you can make them as thick as you want, and even thicken them further if they came out not to your liking initially.

You can still mash potatoes that have been baked (although you'll probably want to peel them), but if you use a wet cooking method, after they're done cooking, drain them and put them back into the pot (still warm, but with the heat off) with the lid off for a minute or two.   Once you don't see any more steam coming off them, check to see if the bottom of the pot is dry .. if it isn't, move the potatoes to another pot (lift them out, to avoid moving the water with them), and drain the water.

I'd personally then dump them back into the now dried pot ... I just find that when you're limiting the amount of moisture going into the potatoes, making sure they stay warm as you're mashing helps the process.  You'll still need some liquid, but making sure that the water is out gives you more control of what liquid is added back in (and you can make sure it's a flavorful liquid ... dairy, olive oil, chicken stock, etc.)