Heat the olive oil and butter in a medium saucepan over medium heat.
Add the orzo pasta to the pan. Toast the orzo, stirring frequently, until it turns golden brown, about 3 to 5 minutes. Watch carefully to prevent burning.
Add the chopped onion to the pan and cook until softened, about 4 minutes.
Add the minced garlic and cook for 1 minute until fragrant.
Add the rinsed rice to the pan. Stir constantly for 2 minutes to coat the grains in fat and lightly toast them. This step helps keep the rice fluffy.
Pour in the chicken broth, salt, and pepper. Bring the mixture to a boil.
Once boiling, immediately reduce the heat to the lowest setting, cover the saucepan tightly with a lid, and simmer for 15 minutes without lifting the lid.
Remove the pan from the heat and let it stand, covered, for an additional 10 minutes. Do not remove the lid during this resting time.
Fluff the rice gently with a fork. Garnish with fresh parsley before serving.