Heat the oil in a saucepan over medium heat.
Add the onion and garlic. Cover and cook until softened, about 5 minutes.
Stir in the mushrooms, cover, and cook 2 minutes more.
Stir in the tamari, thyme and water, and bring to a boil.
Add the cornstarch mixture and cook, stirring until thickened, 2 to 3 minutes.
Decrease the heat to low and stir in the miso paste and pepper to taste.
Pour the gravy mixture into a blender or food processor and puree until smooth.
Return to the saucepan and taste to adjust the seasonings before serving, reheating as necessary. Do not boil.
For a richer brown color, stir in up to ½ teaspoon of browning liquid.
Tightly covered, this sauce keeps well in the refrigerator for up to 4 days and in the freezer for up to 3 months.