Heat the broth and the water in a 2-quart saucepan until simmering; turn the heat to low. Melt 2 tablespoons of the butter in a 12-inch nonstick skillet over medium-low heat. Cook the mushrooms for 3 minutes or until they start to soften. Remove the mushrooms from the skillet to a bowl. Add the remaining butter to the skillet. Cook the onion for 1 minute; stir in the rice. Cook and stir for 2 to 3 minutes or until the rice just starts to brown.
Add the wine; cook and stir until absorbed. Raise the heat to medium (simmering). Add 1 cup of the hot broth mixture. Cook over medium heat until the liquid is absorbed, stirring frequently.
Add the remaining broth 1/2 cup at a time, cooking and stirring each time until the liquid is absorbed. Continue until the broth is used and/or the rice is desired doneness. (Some broth might be left over.)
During the last 2 minutes of cooking, stir in the sour cream, grated Parmesan cheese and thyme leaves. Reserve a few mushrooms for garnish, if desired, and stir in the remaining cooked mushrooms. Garnish the risotto with reserved mushrooms and shaved Parmesan cheese.