Tonight I was Googling cheeseless pizza recipes and saw a potato pizza recipe (which sounds really yummy and I will definitely make it another time). That got me thinking about potato soups and how a really thick potato soup wouldn't be all that different from melted cheese if you flavored it right... it's goopy, it browns on top when you heat it, and the base is almost flavorless and easy to mess around with.
An hour later--including time it took to run out to the store--I had created the best vegan "cheese" sauce I've ever had in my life. It's so simple I'm not even going to cut-tag it.
1 large Idaho potato (would probably be even better with Yukon Golds but my grocery didn't have them)
1/8 cup unsalted roasted cashews
Small pot, strainer, bowl, blender or stick blender
Peel the potato and cut it into small chunks. Place in a small pot with the cashews and add cold water to cover. Boil until very thoroughly cooked. Place the strainer over the bowl and pour in the potatoes and cashews, reserving the cooking water. Put the potatoes and cashews in the blender, or back in the pot if you're using a stick blender. Add in 1/2 cup of cooking water and blend at high speed until very creamy. Add a drizzle of olive oil, nutmeg, and salt to taste, and blend again. If you like nooch, try adding a pinch; it would probably give it a bit of extra depth. Run through the strainer a second time if there are chunks of nuts that the blender didn't catch.
I made a mini pizza with the "cheese" and some arugula, and it was superb: browned on top, still gooey underneath. It would work well on potatoes (that sounds sort of cannibalistic, doesn't it?) or pasta or broccoli--anything you'd make gratinée, basically. Adjust the flavorings to make something closer to cheddar (paprika? cider vinegar? miso paste? mess around and find what works) and it would be killer on nachos. The texture is great for dipping chips or crackers or veggies or slices of apple and pear. If you want to be adventurous, try treating it like curds and see if you can make a solid block of "cheese" out of it! I'll be curious to see what the texture's like after I store it in the fridge.
The major downside of potato "cheese" over soy/nut versions is that it doesn't have much protein. The major upside is that people with soy allergies can eat it! And it is so, so simple to make. Enjoy!