Bring a large pot of salted water to a boil. Add orzo and bring back to a boil. Cook, stirring often, until tender, about 7 minutes.
While orzo cooks, warm 1 Tbsp. oil in a medium skillet over medium-high heat. Add onion and bell pepper and cook, stirring often, until tender, about 8 minutes. Stir in garlic and cook 1 minute longer.
Drain orzo and return to pot. Add remaining 1 Tbsp. oil to orzo and stir to mix. Stir in onion-and-red-pepper mixture and spinach. Season with salt and pepper. Stir over medium-low heat until warmed through, about 2 minutes. Sprinkle with Parmesan and serve.