Puree the tofu with the nondairy milk in a food processor or the container of an immersion blender, until velvety smooth.
Transfer to a small saucepan, then add the remaining ingredients except the salt. Bring to a gentle simmer over medium heat, then cook, stirring frequently, until the cheese has melted, about 5 minutes.
Add a small amount of additional nondairy milk if desired, to make the sauce more fluid. If you’d like, use the immersion blender in the pot to make the sauce even more velvety.
Season with salt (you may not need much, if any), then serve hot over steamed vegetables.