Adjust oven rack to middle position and heat oven to 375°F. Bring water, thyme, bay leaf, whole garlic clove, salt, and baking soda to a boil in a medium saucepan over high heat. Add the rice and return to a boil. Cover the saucepan, transfer to the oven, and bake until the rice is tender, 35 to 50 minutes.

Drain the rice through a fine-mesh strainer set over a liquid measuring cup. Discard the thyme, bay leaf, and whole garlic. Add enough water to the reserved cooking liquid to measure 3 cups total and set aside.

Melt butter in a Dutch oven over high heat. Add the cremini mushrooms, onion, minced garlic, tomato paste, salt, and pepper. Cook, stirring occasionally, until the vegetables are browned and a dark fond (browned bits) develops on the bottom of the pot, about 15 minutes.

Stir in the sherry, scraping up any browned bits from the bottom of the pot, and cook until the liquid has nearly evaporated, about 2 minutes.

Stir in the ground shiitakes, the 3 cups of reserved rice cooking liquid, broth, and soy sauce and bring to a boil. Reduce the heat to low, cover, and simmer until the onion and mushrooms are completely tender, about 20 minutes.

Whisk the cornstarch and water together in a small bowl to create a slurry. Stir the slurry into the soup and simmer until the liquid has thickened, about 2 minutes.

Remove the pot from the heat and stir in the cooked rice, cream, chives, and lemon zest. Cover and let the soup stand for 20 minutes—this allows the rice to absorb the flavors and the texture to stabilize.

Season with additional salt and pepper to taste and serve hot.