Mash artichoke

I am assuming you want to use fresh artichokes, not frozen or canned, as you mention steaming. Artichokes by nature are very fibrous and a whole steamed one would not mash very well. That said, to make a paste from fresh artichokes, I would first steam, then remove all the petals/leaves and all the hair-like choke in the middle. What you would be left with is a mashable disc of soft material attached to the artichoke stem, part of which may be soft enough to mash. Unfortunately, you are going to waste a lot of good artichoke at the base of the petals that is definitely edible, and to me, is the best part of a fresh artichoke. There are recipes on the internet for artichoke pastes that start with canned artichoke hearts that might be easier, especially since you don't have a food processor or blender.