Cover the dried mushrooms with the boiled water and let sit until the mushrooms are tender, about 15 minutes. Chop and reserve any liquid that was not absorbed.
Place broth in a small sauce pan over low heat; bring to a simmer.
Meanwhile, melt 2 tablespoons of the butter in a large, deep skillet over medium heat. Once hot and melted, add the fresh mushrooms, onion, and black pepper; saute until the mushrooms turn tender and release their moisture, about 10-15 minutes.
Add the chopped dried mushrooms, garlic, and thyme; saute until fragrant, about a minute. Add the rice and toast until it starts to turn translucent, about 2 minutes.
Add the wine, deglaze the bottom of the pan by scraping up the browned bits off the bottom of the pan with a wooden spoon. Mix in the reserved mushroom water and stir constantly unit it has been absorbed into the rice.
Begin adding the hot broth, ½ cup at a time. Stir often, until liquid is nearly absorbed. Continue adding ½ cup broth at a time and stirring until absorbed.
Mix in the remaining 1 tablesoon butter and cheese and stir until they have meted.