In a medium saucepan, bring the vegetable broth to a boil over medium-high heat.
Add the orzo pasta to the boiling broth. Cook according to package instructions, usually about 8-10 minutes, or until al dente. Stir occasionally to prevent sticking.
Once cooked, reserve 1/2 cup of the broth and then drain the orzo. Set aside.
In the same pot, heat the olive oil over medium heat. Add the minced garlic and sauté for about 1 minute, until fragrant but not browned.
Stir in the chopped spinach and cook until wilted, around 2-3 minutes.
Add the cooked orzo back into the pot along with the reserved broth. Mix well.
Add the lemon zest, lemon juice, and grated Parmesan cheese. Stir until the cheese is melted and everything is combined.
Season with salt, pepper, and red pepper flakes (if using) to taste.
Remove from heat and let sit for a couple of minutes to allow flavors to meld.