Prepare the potatoes: Boil the diced potatoes in salted water until they are tender, about 12-15 minutes. Drain and set aside.
Sauté the vegetables: In a large skillet, heat olive oil over medium heat. Add the onions and garlic, cooking until softened, about 4 minutes. Add the sliced mushrooms and cook until golden, about 5 minutes. Stir in the spinach and cook until wilted, 2-3 minutes. Season with salt, pepper, and nutmeg.
Mash the potatoes: In a large bowl, mash the boiled potatoes with the heavy cream and vegetable broth until smooth. Stir in the butter and Parmesan cheese.
Combine and bake: Gently mix the sautéed vegetables into the mashed potatoes. Transfer the mixture to a greased casserole dish, spreading it evenly. Top with more Parmesan cheese and bake at 375°F (190°C) for 20-25 minutes, until the top is golden and bubbly.
Garnish and serve: Sprinkle fresh parsley on top for added color and flavor before serving.