In a large pot, bring the vegetable broth to a boil. Add the orzo pasta and cook according to package instructions until al dente, usually about 8-10 minutes. Drain and set aside, reserving 1 cup of the broth.
In the same pot, heat the olive oil over medium heat. Add the minced garlic and sauté for about 1 minute until fragrant.
Add the fresh spinach to the pot and cook until wilted, about 2-3 minutes.
Stir in the heavy cream, reserved broth, lemon zest, and lemon juice. Bring to a gentle simmer.
Add the cooked orzo and grated Parmesan cheese to the pot. Stir until well combined and the cheese has melted. Season with salt and pepper to taste.
Remove from heat and let it sit for a couple of minutes to thicken. Serve warm, garnished with fresh parsley.