Melt butter in a large stockpot or Dutch oven over medium high heat. Add mushrooms and shallots. Cook, stirring often, until tender, about 8 minutes.
Stir in garlic until fragrant, about 1 minute; season with salt and pepper, to taste. Set aside 1 cup mushroom mixture; keep warm.
Stir in rice and thyme, stirring constantly, until lightly toasted and fragrant, about 1-2 minutes.
Stir in wine, stirring constantly and scraping any browned bits from the bottom of the Dutch oven, until almost completely absorbed, about 1-2 minutes.
Reduce heat to low. Stir in 1 cup stock mixture. Cook, stirring constantly, until almost completely absorbed.
Continue adding remaining stock mixture, 1/2 cup at a time, stirring constantly and waiting until almost completely absorbed before adding additional stock mixture, until al dente, about 20 minutes.
Stir in Parmesan; season with salt and pepper, to taste.
Serve immediately with the reserved mushroom mixture and additional Parmesan, if desired.
for the stock mixture
Heat chicken stock and 1 teaspoon salt in a large stockpot or Dutch oven over medium high heat. Bring to a boil; reduce heat and simmer.