After soaking, drain and rinse the almonds under cool water.
In a blender, combine the soaked almonds and filtered water.
Blend on the highest setting for 2 minutes. The almonds should be broken down into a fine meal, and the water will turn white and opaque.
Line a bowl with a nut milk bag, cheese cloth, or a thin dish towel (you can also use a fine-mesh strainer).
Pour the almond mixture into the lined bowl.
Gather the cloth or bag around the almond meal and twist it close. Squeeze and press with clean hands to extract as much almond milk as possible. You should get about 2 cups.
Pour the milk back into the blender and add the sweetener, vanilla extract, and salt. Blend to combine.
Store the almond milk in sealed containers in the fridge for up to two days. Shake well before drinking, as it may separate over time.