In a small saucepan, heat chicken or vegetable broth until hot. Keep warm over medium heat.
Add olive oil, one tablespoon butter, and garlic to a cold saucepan. Turn heat to medium and sauté for approximately one minute, or until garlic becomes softened.
Add onion and sauté for 2 minutes before adding the sliced mushrooms. Cook mushrooms until they soften and release liquid, approximately 4 or 5 minutes.
Remove from heat and season with salt and pepper, to taste. Transfer to a bowl and keep warm.
Return pan to the heat and add remaining butter.
Add Arborio rice and sauté for 1-2 minutes until thoroughly coated.
Add white wine and stir constantly until the wine is completely absorbed.
Add a ladleful of the warm broth to the pan and stir constantly until it is completely absorbed.
Continue to add the broth a ladleful at a time, stirring as before until all of the broth has been incorporated and the rice has a rich, creamy consistency. This should take around 25-30 minutes. (If you want a creamier texture, add more broth until you achieve the results you desire).
Remove the risotto from the heat and stir in the Parmesan and rosemary.
Add the mushroom mixture to the pan and stir thoroughly until combined.
Season to taste with salt and pepper.
Transfer to a serving dish and sprinkle with additional fresh rosemary, if desired. Serve immediately.