Important: You’ll want to use a jar or other container that is just slightly wider than the head of the immersion blender. If the container is too wide, it may not blend properly.
Add the soy milk, along with the Dijon, vinegar, lemon juice, and (optional) minced garlic to the jar. Place the immersion blender in all the way, so it touches the bottom of the jar. Now check that the level of the liquids is high enough to be in contact with the blades. If not, you may wish to double the recipe to ensure it blends properly.
Add the oil to the container all at once and allow it to sit for about 30 seconds.
With the head of the immersion blender in firm contact with the bottom of the jar, begin blending on high. The oil will be gradually pulled in and blended with the soy milk mixture.
After about a minute, once the mixture starts to thicken, you can slowly lift or tilt the head of the immersion blender while still blending to incorporate more of the oil gradually until all of it is emulsified. Blend just until it is thick enough, as over-blending can cause the emulsion to break.
Add salt and adjust other flavors to taste.