Bring a large pot of salted water to a boil. Add the orzo pasta and cook according to package instructions until al dente, about 8-9 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 occasionally, until wilted, about 3-4 minutes.
Pour in the heavy cream and chicken broth, stirring to combine. Bring the mixture to a gentle simmer.
Add the cooked orzo to the skillet and stir well to combine with the creamy spinach mixture.
Stir in the grated Parmesan cheese until melted and the sauce is creamy.
Season with salt, black pepper, and crushed red pepper flakes. Stir well and cook for an additional 2 minutes to heat through.
Remove from heat and serve immediately.