Warm the broth in a small saucepan over low heat. In a wide sauté pan, heat 1 tablespoon of the oil over medium-high heat. Brown the sliced mushrooms in two batches, stirring occasionally, until their released moisture evaporates and edges turn golden, about 6–8 minutes per batch. Transfer to a bowl.

Reduce the heat to medium. Add the remaining tablespoon of oil and the onion to the same pan. Cook for about 5 minutes until softened. Stir in the garlic for 30 seconds, then add the rice and stir for 2 minutes until the grains are lightly coated and their edges begin to look translucent.

Pour in the wine and stir until mostly absorbed, about 1–2 minutes. Add a ladle of warm broth and maintain a steady simmer. Stir often, adding another ladle when the previous liquid is mostly absorbed. Continue for about 18–24 minutes, until the rice is tender with a slight bite and no chalky center. Use more or less broth according to texture.

Stir the browned mushrooms and thyme into the rice during the final 3–4 minutes, adding broth to keep the mixture loose.

Take the pan off the heat. Stir in the butter, Parmesan and black pepper. Add a little warm broth or hot water if needed so the risotto flows softly when the pan is tilted. Taste before adding salt. Divide among four warm shallow bowls and serve promptly.