Heat 2 tablespoons water in a large soup pot and add onions. Cook over medium-high heat until onions are soft.
Add vegetable broth, sliced mushrooms, paprika, dill, caraway seeds (if using), and black pepper. Lower the heat slightly and cook 5 minutes more, stirring frequently.
Add soy sauce or tamari.
In a separate pan, mix ΒΌ cup milk with flour to form a paste. Cook over medium heat, stirring constantly, for 1 minute. Then whisk in the remaining soy milk and cook until steamy and slightly thickened.
Add the milk-flour mixture to the soup. Stir in the lemon juice (and wine, if using) just before serving.