Heat the broth in a separate saucepan and keep it at a bare simmer. Prepare the mushrooms and finely dice the onion before starting the rice; the risotto needs attention once liquid is added.

Heat oil in a wide heavy saucepan over medium-high heat. Add half the mushrooms in a loose layer and cook for 5–6 minutes, turning occasionally, until browned. Transfer to a plate and repeat with the rest, adding a small splash of oil only if the pan is dry. Season with the measured salt.

Lower heat to medium. Melt 1 tablespoon butter in the same pan and cook onion for about 5 minutes until soft. Add garlic for 30 seconds. Stir in rice for 1–2 minutes until coated and lightly translucent at the edges. Add wine or the extra broth and stir until mostly absorbed.

Add warm broth about 1/2 cup at a time, stirring frequently and adding more when the previous addition is mostly absorbed. Keep a gentle simmer, not a fierce boil. After about 18 minutes, start tasting a grain. Continue until the rice is tender with a slight bite, usually 20–25 minutes total; use only as much broth as needed.

Stir in mushrooms and thyme during the final 2 minutes. Remove from heat, add remaining butter and Parmesan, and stir until glossy. Add a little warm broth so it flows slowly when spooned. Rest for 2–3 minutes, taste for salt and pepper, and serve at once.