Place the rinsed and drained rice in the bowl of a rice cooker. Drizzle with 1 tablespoon of the olive oil and stir to coat well. Add 2 1/2 cups of broth and the salt. Stir well.

Close the lid of the rice cooker and press the "Cook" button. Cook for 20 minutes, then switch to the "Keep Warm" setting.

While the rice is cooking, heat the remaining 1 tablespoon of olive oil in a large, heavy skillet over medium heat. Add the onion and cook, stirring frequently, until tender, about 5 minutes.

Add the garlic and saute, stirring continuously, for another minute or two.

Add the mushrooms and pepper. Cook, stirring continuously, until the mushrooms are juicy and tender, 5 to 8 minutes. Remove the skillet from the heat. Taste and, if necessary, add salt and additional pepper, to taste. Set aside.

After switching the rice cooker to the "Keep Warm" setting, carefully open the lid and stir in the sauteed mushrooms, and additional 1/2 cup of the broth, the butter, parsley, and Parmesan cheese. The mixture should have a creamy consistency; but, if it does not, stir in up to another 1/2 cup of the broth.

Continue stirring for about 1 minute longer; then, taste and adjust the seasonings again, if necessary. Serve with additional Parmesan cheese for garnish, if desired.