Heat the vegetable broth in a saucepan over low heat and keep it warm.
Warm the olive oil and 1 tablespoon of butter in a large skillet over medium heat. Add the onion and cook until soft.
Stir in the garlic and cook for one minute, then add the sliced mushrooms. Cook until the mushrooms release their liquid and start to brown.
Add the Arborio rice and stir to coat the grains with the oil and butter. Pour in the white wine and cook until it is mostly absorbed.
Add the warm broth one ladle at a time, stirring often and waiting until each addition is absorbed before adding the next. Continue until the rice is creamy and tender.
Remove the skillet from the heat. Stir in the remaining 2 tablespoons of butter, the Parmesan cheese, and the thyme leaves. Season with salt and pepper.
Spoon the risotto into four bowls and serve at once.