In a small bowl, combine cornmeal, salt, black pepper, and Italian parsley. Mix well.
Lightly dredge each of the polenta slices in the cornmeal mixture, pressing gently to ensure an even coating.
Heat 1 tablespoon olive oil and 1 tablespoon butter in a large skillet over medium heat. Place the polenta rounds in an even layer and cook for 5-10 minutes per side until golden brown. Transfer the polenta to a paper towel-lined plate, and wipe any residual cornmeal from the pan.
In the same skillet, add the remaining 2 tablespoons of olive oil. Once hot, add the chopped yellow onion and sliced mushrooms. Sauté for 3-5 minutes until they’re soft and fragrant. Stir in the minced garlic along with additional salt and pepper to taste, cooking for an additional 1 minute.
Add the Marsala wine and vegetable broth. Bring the mixture to a boil, then reduce the heat to low and let it simmer, uncovered, for 15 minutes. Adjust seasoning to taste then stir in the additional Italian parsley.
Arrange the crispy polenta rounds on a plate, generously spoon the marsala mushroom sauce over the top, and serve hot.