In large stock pot heat olive oil on a propane stove over medium-low heat.
Add onion and leeks. Cover and cook till soft, about 10-12 minutes, stirring frequently.
Uncover and stir in brown sugar. Cook and stir for 2-4 minutes or until golden brown. Do not let it burn!
Stir in mushrooms and carrots. Cook uncovered, over medium heat for 15-20 minutes, until vegetables are tender.
Stir in vegetable broth, cooking wine and seasonings.
In screw-top jar, combine the cold water and flour and cover. Shake well until combined and smooth. Add to the soup mixture and stir in. Cook and stir until slightly thickened and bubbly. Cook a few minutes more over medium-low heat.
With a stick blender, do some processing in pot on 1/3 of the soup mixture to smooth and thicken. This gives the soup a silkier texture. For chunkier soup skip this step.
Add the cooked rice to desired volume.