Place the almonds and 3¼ cups of the cold water in a medium bowl. Cover and let the almonds soak at room temperature for 8 hours, or overnight.
Drain the almonds and discard the water.
Place the almonds and 3¼ cups of fresh cold water in a blender. Add the pitted dates, vanilla, cinnamon and salt and blend the mixture until it is as smooth as you can get it, at least 2 minutes.
Set a large, very fine sieve over a deep bowl. Pour half the almond mixture into the sieve. Let it drain 5 minutes, then use the back of a spoon to push on the almond mixture to extract and push all the liquid out of it, through the strainer, and into the bowl below.
Remove the drained almond mixture from the strainer. (Place the drained almond mixture in another bowl, cover, refrigerate and keep for another use, such as blending into your morning oatmeal, or to use in a crumble topping.)
Set the sieve back over the bowl and strain the remaining blended almond mixture in the same way you did the first batch.