In a large pot, bring salted water to a boil. Add the tortellini and cook according to package instructions until al dente. Drain and set aside.
In the same pot, heat the olive oil over medium heat. Add the diced onion and cook until translucent, about 3-4 minutes.
Stir in the minced garlic and sliced mushrooms, cooking for an additional 4-5 minutes until the mushrooms soften and release their moisture.
Add the chopped spinach and cook until wilted, about 2 minutes.
Pour in the vegetable broth and bring to a simmer. Allow to cook for 2-3 minutes to reduce slightly.
Lower the heat and add the heavy cream, stirring to combine. Allow the sauce to warm through, and season with salt, pepper, and a pinch of nutmeg if desired.
Mix in the grated Parmesan cheese, ensuring it melts smoothly into the sauce.
Add the cooked tortellini to the pot and gently toss to coat them well in the creamy sauce. Cook for an additional 1-2 minutes to heat through.
Remove from heat and serve immediately, garnished with fresh parsley if desired.