In a large pot, bring the vegetable broth to a boil. Add the orzo and cook according to package instructions until al dente, about 8-10 minutes. Drain and set aside, reserving 1/2 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.
Reduce the heat to low and stir in the heavy cream, reserved broth, lemon zest, and lemon juice. Mix well and let it simmer for 2-3 minutes.
Add the cooked orzo and grated Parmesan cheese to the pot. Stir until the cheese is melted and the orzo is well coated. Season with salt and pepper to taste.
Serve warm, garnished with fresh chopped parsley.