After grating the potatoes, squeeze out as much moisture as you can. If you prefer, strain the grated potatoes in a colander, let them sit for a few minutes, pour off the clearer liquid and add the thicker potato starch to the mixture.
Put the grated and drained potatoes, flour, green onion, nondairy milk, cornstarch, salt and pepper in a bowl and mix well.
Preheat 1/4" to 1/2" of vegetable oil in a large skillet (preferably cast iron) over medium heat.
While the oil heats, ready the cooling racks by putting them on a paper towel-lined surface.
Spoon a generous 1/4 cup of the potato mixture into the pan and flatten to about a 1/4" thickness with a spatula. Fry until golden brown, flip and do the same on the other side.
Remove the cooked latkes to the cooling racks.