In a large pot, heat the olive oil over medium heat. Once hot, add the diced onion and sauté for about 3-4 minutes until it becomes translucent. Add the minced garlic and cook for an additional minute, stirring often to prevent burning.
Next, toss in the sliced mushrooms and continue to sauté for another 5-7 minutes. The mushrooms will release their moisture and become tender. Stir occasionally to ensure they cook evenly.
Once the mushrooms are cooked, add the orzo pasta to the pot. Stir well to coat the pasta with the oil and sautéed vegetables. Pour in the vegetable broth and bring the mixture to a boil. Reduce heat to a simmer, cover the pot, and cook for about 10-12 minutes, or until the orzo is al dente.
When the orzo is nearly done, stir in the fresh spinach and heavy cream. Mix well until the spinach wilts down and everything is heated through. This should take about 2-3 minutes.
Remove the pot from the heat and stir in the grated Parmesan cheese. Season with salt and pepper to taste. The cheese will melt and create a deliciously creamy sauce that clings to the orzo.