Heat the olive oil and butter in a 12" skillet over medium heat until the butter melts, about 30 seconds.
Add the chopped onion and minced garlic and cook, stirring occasionally, until the onion is softened and the garlic is fragrant, about 2 minutes.
Stir in the dry orzo and cook in the oil and butter for about 2 minutes, stirring, until the orzo is lightly toasted.
Season with the salt and pepper, then pour in the chicken broth and half-and-half. Increase heat to bring the mixture to a boil.
Once boiling, reduce heat to medium-low, cover, and simmer for 5 minutes until the orzo is tender and most liquid is absorbed.
Remove the lid, stir in the grated Parmesan and chopped parsley until the cheese melts and the sauce is creamy; adjust seasoning if needed.
Serve immediately.