In a large skillet, heat oil or butter over medium heat. Add the chopped onion and cook until soft and translucent, about 4-5 minutes.
Stir in the garlic and cook for another 30 seconds until fragrant.
Pour in the orzo and stir for a minute to toast slightly.
Add the broth, cream, and salt. Bring to a simmer and reduce heat to low.
Cook uncovered, stirring frequently, until the orzo is tender and most of the liquid is absorbed, around 10 minutes.
Stir in lemon zest, lemon juice, and Parmesan. Adjust seasoning if needed.
Garnish with fresh parsley and serve warm.