Heat the olive oil in a shallow saucepan over medium heat until shimmering.
Add the orzo and sauté, stirring frequently, until the orzo turns golden brown but not burnt, about 2–4 minutes.
Add the butter and stir until melted, then add the rinsed and drained rice and cook 2–3 minutes, stirring to coat the rice in oil and butter.
Pour in the hot chicken broth and add the salt; stir to combine.
Increase heat to bring the mixture to a boil, then reduce heat to low, cover, and simmer until small holes appear on the rice surface, about 10–12 minutes.
Turn off the heat and let the pilaf rest, covered, for 5 minutes. Fluff gently with a fork.
Cover and let rest an additional 10 minutes, then stir gently before serving.