After soaking the almonds overnight, drain off the soaking water and rinse them thoroughly under cool running water to remove any residue. The almonds should feel slightly plump and softened between your fingers.
Transfer the soaked almonds to a high-powered blender. Add the cold filtered water, then include the vanilla, sweetener of choice, and sea salt if using.
Blend on high for about 2 minutes, or until the mixture looks thick, frothy, and the almonds have broken down completely. The liquid should appear creamy and opaque with no large almond pieces remaining.
Set a nut-milk bag or a few layers of cheesecloth over a large bowl or measuring jug. Carefully pour the blended mixture through the bag or cloth, then gently squeeze and press to extract as much smooth almond milk as possible, leaving the dry pulp behind.
Pour the strained almond milk into a clean, airtight glass bottle or container. Refrigerate and chill before serving, and use within 3 days, giving the container a good shake before each pour as some natural separation may occur.