Cook the penne pasta according to package instructions until al dente. Drain and set aside.
In a large skillet, heat the olive oil over medium heat. Add the diced onion and sauté for about 3-4 minutes until translucent.
Stir in the minced garlic and sliced mushrooms. Cook for an additional 5-7 minutes, until the mushrooms are tender and browned.
Add the fresh spinach to the skillet and cook until wilted, about 2 minutes.
Season the mixture with dried oregano, salt, and black pepper.
Pour in the heavy cream and chicken or vegetable broth. Stir to combine and bring to a simmer.
Add the cooked penne pasta to the skillet and toss everything together until well coated.
Remove from heat and stir in the grated Parmesan cheese until melted and creamy.
Garnish with fresh parsley before serving.