Saute the mushrooms in the oil on medium-high until they are soft and dark, about 20 minutes. You can also simmer the mushrooms in the red wine, but the flavor won’t be quite as rich.
Add the garlic and onions, and thyme/marjoram if you’re using it. Leave this on the heat, stirring occasionally, until the onions are translucent and slightly browned.
Once the vegetables are cooked, keep the heat up to deglaze the pan with red wine. Add the balsamic vinegar and water, along with a pinch of salt to bring the flavors together. Let this simmer, the longer the better.
Dissolve the arrowroot or kuzu (or flour) in a small amount of cool water. Stir it into your gravy, heating until it’s nearly boiling. Keep stirring occasionally until it thickens.
If you want a smooth gravy, puree.