With a handheld mixer or in a stand mixer with the paddle attached, cream together the "butter", shortening, sugar and cream cheese until light and fluffy, around 2-3 minutes. Use a rubber spatula to scrape down the sides a few times in between to ensure everything is evenly mixed.
Add the vanilla extract and mix in.
Take the bowl off the stand mixer, and add the flour and 2 tbsp of soy or nondairy milk.
Using a fork, mix, adding a tiny bit of milk as necessary, until you have a cohesive ball of dough. Don't overwork the dough -- stop mixing as soon as the dough comes together. I needed almost the entire ½ cup of milk because I was making these on a very cold, dry day, but how much milk you add will vary depending on your weather. In a very moist kitchen you might not need any milk at all.
Divide the dough into two halves. Using the palms of your hands, roll each half into a smooth log, about six inches in length and 1 ¾ inches in diameter. Wrap a piece of parchment paper around each log and twist the ends tightly, like a piece of candy.
Refrigerate both logs for at least an hour so they firm up. Mine never firmed up where I could cut them easily with a knife into rounds, so I'd advise even freezing them in the last 15 minutes of chilling so you can cut perfectly round cookies.
Preheat your oven to 350 degrees.
Take the chilled log of dough and using a very sharp knife slice into 12 round cookies. Repeat with the second log.
Place the cookies about 1-inch apart on a baking sheet (you can spray lightly with some oil, if you like, but I found these cookies don't stick because of their high fat content). Sprinkle the tops of the cookies with some granulated sugar.
Bake, one sheet at a time, until the cookies are lightly golden brown around the edges. It took me nearly 25 minutes in my oven, but because ovens are highly quirky gadgets with minds of their own, start checking 15 minutes after baking. If the cookies are turning color around the edges, take them out. You don't want highly colored cookies because they will be too tough which shortbread should never, ever be.
Transfer the cookies to a rack with a spatula and cool thoroughly before eating.