For the polenta: Heat one tablespoon of the olive oil in a medium saucepan over medium heat. Add the onions and cook for 4-5 minutes or until softened. Add the garlic and cook for 30-60 seconds or until fragrant but not brown.
Add the chicken broth and bring to a boil. Slowly stir in the polenta. Reduce heat to a very low simmer and cook, uncovered, stirring occasionally, for approximately 10-15 minutes or until the polenta has thickened. (I like there to be a little soupiness remaining, as the polenta will continue to thicken as it sits. At this point you may also season to taste; depending on broth used, you may wish to add no salt or up to ½ teaspoon or so.)
When the polenta is finished cooking, remove from the heat and stir in the Parmesan cheese.
For the mushrooms: Meanwhile, in a medium sauté pan, heat the other tablespoon of oil over medium heat. Add the mushrooms and sauté for 8-10 minutes, stirring occasionally, or until their liquid has been released and the mushrooms are golden brown. Season with salt and pepper. (Here, I use about ¼ teaspoon of each.)
Serve: You may stir in the mushrooms or top the polenta with them. Sprinkle with chopped fresh parsley and enjoy!