Bring a large pot of salted water to a boil. Add the orzo pasta and cook according to package instructions until al dente, about 8-10 minutes. Drain and set aside.
In a large skillet, melt the butter over medium heat. Add the minced garlic and sauté for 1 minute until fragrant.
Add the chopped spinach to the skillet and cook, stirring frequently, until wilted, about 2-3 minutes.
Pour in the vegetable broth and heavy cream, stirring to combine. Bring the mixture to a gentle simmer.
Add the cooked orzo to the skillet and stir well to coat the pasta with the creamy sauce.
Stir in the grated Parmesan cheese, salt, black pepper, and crushed red pepper flakes. Continue cooking for 2-3 minutes until the sauce thickens slightly and the cheese is melted.
Remove from heat and serve immediately.