Heat the broth in a small pot over low heat. Turn off the heat and cover to keep warm.

Set a medium size pot over medium heat and add 1 tablespoon of butter. When the butter is melted, add the sliced mushrooms. Cook for 2 minutes, stirring frequently until softened. Transfer the cooked mushrooms to a bowl and set aside. Return the pot to the stove.

Add the remaining 1 tablespoon of butter. When it is melted, add the chopped onion. Cook for 3 minutes, until softened. Add the garlic and continue cooking for an additional 30 seconds.

Add the Arborio rice, thyme, and black pepper; stir to combine. Stir frequently for about 2 minutes, until the rice smells lightly toasted.

Pour in the white wine and stir until it's mostly absorbed, about 1 minute.

Gradually add the warm broth, 1/2 cup at a time, stirring frequently. Wait until each 1/2 cup is absorbed before adding the next. Continue until you have used all the broth and the rice is creamy and al dente, about 20 minutes.

Stir in the reserved mushrooms and Parmesan cheese.

Adjust seasoning to taste and serve hot.