Add the first 5 ingredients (1 whole garlic, ¾ tsp salt) into a Dutch oven and bring to a boil. Add in baking soda and rice and return to a boil. Cover and place in oven at 375°F for 40 minutes, or until rice is tender. Set a strainer over a 4 cup measuring cup and pour rice mixture through strainer. Add more water to bring the level up to 3 cups, and set aside along with the rice (discarding the bay leaf and garlic).
Add the butter to the pot and melt over medium high heat, along with the pepper, chopped mushrooms and onions. After 5 minutes, reduce heat to medium and add the tomato paste and remaining ¾ tsp salt and 2 minced cloves of garlic. Continue cooking for another 10 minutes until veggies are browned and a dark fond develops on bottom of pot (this is why you want to use a heavy bottomed pot like a Dutch oven – the fond will build up on the bottom but will not burn).
Deglaze the pot by whisking in the sherry, stirring to scrape up all the bits stuck to the bottom of the pot, until the sherry is nearly evaporated. Stir in dried mushrooms, broth, soy sauce, along with reserved liquid from cooking rice and bring to a boil. Cover and reduce heat to a simmer, cooking for another 20 minutes.
In a small dish whisk together cornstarch with ¼ cup of cold water, then add to soup, stirring until soup thickens. Turn heat off and stir in cream, chives, lemon zest and reserved wild rice. Cover an set aside 10 minutes to allow rice to reheat in soup.