1) Heat 1/2 cup of water in a large pot and add the onions. Cook over high heat, stirring often, until the onions are soft and all the water has evaporated, about 5 minutes. Add another 1/4 cup of water, stir to loosen any bits of onion stuck to the pan, and continue cooking until most of the water has evaporated and the onions begin to brown, about 3 minutes.
2) Add the mushrooms and spices. Slightly lower the heat, cover, and cook 5 minutes, stirring frequently.
3) Add the soy sauce and water or vegetable stock. Cover and simmer about 10 minutes.
4) 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 vegan milk and cook over medium heat, stirring frequently, until steamy and slightly thickened.
5) Add the vegan milk mixture to the soup. Stir in the lemon juice just before serving.
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