Into a small mixing bowl, add cornmeal, salt, pepper, and parsley. Stir to mix well.
Dredge each polenta round in the cornmeal mixture, pressing lightly to ensure an even coating.
Into a large skillet over medium heat, add olive oil and butter. When butter is melted, add the polenta rounds in an even layer.
Cook polenta 5-10 minutes on each side, or until golden brown. Remove to a paper towel-lined plate. Remove any cornmeal residue from the pan.
To the same skillet, add remaining 2 tablespoons of olive oil. Once oil is hot, add onions and mushrooms. Sauté 3-5 minutes, until soft and fragrant.
Add garlic, salt, and pepper. Continue cooking and stirring another 2-3 minutes.
Pour in the wine and broth. Bring to a boil, the reduce heat to low. Simmer, uncovered, for 15 minutes.
To serve:
Arrange polenta rounds on a plate then with mushroom sauce. Serve hot.