Finely grate the ginger over a small bowl.
Place the grated ginger into a fine-mesh strainer and press firmly with the back of a spoon to extract about 1 teaspoon (5 ml / 0.2 fl oz) of pure ginger juice.
Discard the pulp.
Combine the ginger juice, walnuts, miso, and optional soy sauce in a high-speed blender.
Blend on high until the mixture is completely smooth and creamy, stopping to scrape down the sides of the blender as needed.
Check the consistency. If the sauce is too thick, add a teaspoon of water or soy sauce at a time and blend again until it reaches your desired thickness.
Serve immediately or transfer to an airtight container and refrigerate for up to 3 days.