Bring a large pot of salted water to a boil and cook the orzo until it is tender but still firm. Drain and set it aside.
Warm the olive oil in a medium pot over medium heat.
Add the chopped green onions and garlic to the oil and cook for about one minute, stirring occasionally, until the onions soften and the garlic releases its aroma.
Season with salt and pepper and stir everything together.
Sprinkle in the flour and stir thoroughly, letting it cook for about half a minute to remove the raw taste.
Gradually pour in the milk while whisking continuously to prevent lumps. Keep cooking and stirring until the sauce thickens and gently simmers, about 5 to 8 minutes.
Fold in the chopped spinach and mix well to combine with the sauce.
Stir in the parmesan cheese until it melts fully and forms a creamy sauce.
Add the cooked orzo back into the pot and toss gently to coat the pasta completely with the sauce. Remove from heat and serve straight away.