Melt butter in a dutch oven over high heat. Add fresh mushrooms, onion, garlic, tomato past, ¾ tsp kosher salt, and 1 tsp fresh ground black pepper. Cook, stirring occasionally, until veggies are browned and dark fond forms on bottom of pot, approx 15 minutes.
Add sherry, scraping up any browned bits and cook until reduced and pot is almost dry, about 2 minutes. Add ground shiitake mushrooms, reserved rice cooking liquid, stock or broth, and soy sauce; bring to a boil. Reduce heat to low and simmer, covered until veggies are tender, about 20 minutes.
Add ground shiitake mushrooms, reserved rice cooking liquid, stock or broth, and soy sauce; bring to a boil. Reduce heat to low and simmer, covered until veggies are tender, about 20 minutes.
Whisk cornstarch and ¼ cup cool water in a small bowl or measuring cup. Stir into soup thoroughly, return to simmer and cook about 2 minutes until thickened. Remove soup from heat and add cooked rice, chives, cream and lemon zest, stirring well to incorporate. Cover pot and let sit 20 minutes before serving.