To brown and soften the onions, heat ½ cup of water or vegetable stock in a large pot and add the onions.
Cook over high heat, stirring often, until the onions are soft and all the liquid has evaporated, about 5 minutes.
Add another ¼ cup of water or vegetable stock, stir to loosen any bits of onion that have stuck to the pan, and continue cooking until most of the liquid has evaporated and onions begin to brown, about 3 minutes.
Add the sliced mushrooms and spices.
Lower the heat slightly, cover and cook 5 minutes, stirring frequently.
Add the soy sauce and stock.
Cover and simmer 10 minutes.
In a separate pan, mix the olive oil and flour to form a thick paste.
Cook, stirring constantly, for 1 minute then whisk in the soy milk or rice milk and cook over medium heat, stirring frequently, until steamy and slightly thickened.
Add the milk mixture to the soup.
Stir in the lemon juice and red wine just before serving.