Place the almonds in a medium bowl and cover with 2 cups cold water. Cover with plastic wrap and refrigerate until softened and plump, at least 8 hours but preferably overnight.
Drain the almonds through a fine-mesh sieve, then rinse well. Reserve the sieve for later. Transfer the almonds to a blender and add 2 cups fresh cold water. Blend on high until very smooth, about 2 minutes. It's okay if the mixture looks slightly grainy.
Line the reserved sieve with a clean kitchen towel or cheesecloth and place over a medium bowl. Working in batches, pour the blended almond mixture through the cloth in the sieve, separating the almond milk from any grainy bits. Gather the edges of the towel together and use your hands to squeeze out any remaining milk.
Whisk in 1 teaspoon vanilla and/or 1 to 2 tablespoons honey or maple syrup if using to flavor and sweeten the almond milk. Serve immediately or refrigerate in an airtight container for up to 5 days.