In a large saucepan, 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 saucepan, melt the butter over medium heat. Add the minced garlic and sauté for about 1 minute until fragrant.
Add the sliced mushrooms to the pan and cook for 5-7 minutes, stirring occasionally, until they are browned and tender.
Stir in the fresh spinach and cook until wilted, about 2-3 minutes.
Return the cooked orzo to the saucepan and mix well with the mushrooms and spinach. Pour in the reserved broth and season with salt, black pepper, and red pepper flakes if using. Stir to combine and heat through for another 2 minutes.
Remove from heat and stir in the grated Parmesan cheese until melted and creamy.
Serve warm, garnished with chopped parsley.