Bring the vegetable or chicken broth to a boil in a medium saucepan. Add the orzo pasta and cook according to package instructions until al dente, usually about 8-10 minutes.
Once the orzo is cooked, reserve about a half cup of the broth, then drain the remaining broth and set the orzo aside.
In the same saucepan, melt the unsalted butter over medium heat. Add the minced garlic and sauté for about 1 minute until fragrant, being careful not to burn it.
Pour in the heavy cream and the reserved broth, stirring well to combine, and bring the mixture to a gentle simmer.
Stir in the grated Parmesan cheese until it melts completely and the sauce is creamy. Add the cooked orzo to the saucepan and mix until the pasta is evenly coated.
Season with salt and black pepper to taste. Continue to cook for another 2-3 minutes, allowing the sauce to thicken slightly.
Serve in a dish and garnish with chopped fresh parsley before serving.