Cook the Potatoes: In a large pot, bring salted water to a boil. Add the potatoes and cook for 10-12 minutes, or until just fork-tender. Drain and set aside.
Sauté the Onion and Mushrooms: In a large skillet over medium heat, add a splash of oil or butter and cook the chopped onion until translucent, about 3-4 minutes. Add the sliced mushrooms and cook until browned and softened, about 5 minutes.
Add Garlic and White Wine: Stir in the minced garlic and cook for 1 minute, then add the white wine (if using). Let the wine simmer for 2-3 minutes to reduce slightly, intensifying the flavor.
Prepare the Cream Sauce: Pour in the heavy whipping cream, stirring well. Add the grated Parmesan cheese, salt, and pepper, and continue to stir until the cheese is melted and the sauce is creamy and smooth, about 3-5 minutes.
Combine with Potatoes and Garnish: Add the cooked potatoes to the skillet, stirring gently to coat them in the creamy sauce. Let everything simmer together for another 2-3 minutes, allowing the flavors to meld. Sprinkle with fresh parsley before serving.