Heat the olive oil in a medium saucepan over medium heat.
Add the orzo and sauté, stirring frequently, until the orzo turns golden brown and fragrant, about 2–3 minutes.
Add the butter and stir until melted, then add the rinsed and drained rice and cook, stirring constantly, for 2–3 minutes to coat the rice with the oil and butter.
Carefully 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 and liquid is absorbed, about 10–12 minutes.
Turn off the heat and let the pilaf rest, covered, for 5 minutes. Uncover and gently fluff the rice with a fork.
Cover again and let rest for another 10 minutes, then stir gently before serving.