Heat the olive oil in a shallow pot over medium heat. Add the orzo pasta and cook until it turns golden brown, stirring frequently to prevent burning.
Add the butter to the pot. Once melted, add the rinsed and drained rice. Cook for 2-3 minutes, stirring constantly to coat the rice with the oil and butter.
Pour in the hot chicken broth and add the salt. Stir well. Increase the heat to bring the mixture to a boil.
Once boiling, reduce the heat to low, cover the pot with a lid, and simmer until small holes appear on the surface of the rice, about 10-12 minutes.
Turn off the heat and let the rice pilaf rest with the lid on for 5 minutes. Then, fold the rice with a fork to fluff it up. Cover again and let it rest for another 10 minutes.
Stir the rice pilaf gently before serving. Enjoy as a side dish with salad, yogurt, pickles, or your choice of protein such as chicken, meat, meatballs, beans, or chickpea stew.