In a large pot, bring salted water to a boil. Add the orzo and cook according to package instructions until al dente, usually about 8-10 minutes. Drain and set aside.
In the same pot, heat the olive oil over medium heat. Add the diced onion and sauté until translucent, about 3-4 minutes.
Stir in the minced garlic and cook for an additional 1 minute until fragrant.
Add the fresh spinach to the pot, and sauté until wilted, about 2-3 minutes.
Pour in the vegetable broth and bring to a gentle simmer.
Stir in the heavy cream, allowing the mixture to combine thoroughly.
Add the cooked orzo to the creamy spinach mixture, and mix well.
Fold in the grated Parmesan cheese and season with salt, pepper, and nutmeg (if using). Cook for another 2-3 minutes until heated through.
Remove from heat and garnish with chopped fresh parsley before serving.