Heat broth in a medium saucepan; keep warm over low throughout cooking.
Heat 2 tablespoons oil in a large skillet over medium-high; sauté mushrooms about 5 minutes until golden. Salt and set aside.
Add remaining 1 tablespoon oil to same skillet; cook onion about 3 minutes until soft. Stir in rice 1 minute until lightly toasted.
Add wine; stir until absorbed. Add warm broth a ladle at a time, stirring frequently and letting each absorb before adding more.
Continue about 20 minutes, until rice is creamy and tender with a slight bite.
Remove from heat; stir in mushrooms, Parmesan, cold butter, and truffle oil until creamy and combined.
Season with salt and pepper; serve immediately with thyme and extra Parmesan, if desired.