Heat a large skillet over medium-low heat and melt the butter.
Add the orzo to the melted butter and cook, stirring frequently, until the orzo is golden brown.
Stir in the diced onion and continue to cook until the onion is translucent and soft, about 3–4 minutes.
Add the minced garlic and cook for 1 minute, stirring, until fragrant.
Stir in the uncooked white rice, then pour in the chicken broth and increase heat to bring to a boil.
Once boiling, reduce heat to medium-low, cover the skillet, and simmer until the rice is tender and the liquid is absorbed, about 20 to 25 minutes.
Remove the skillet from heat and let it stand, covered, for 5 minutes to finish cooking with residual heat.
Fluff the pilaf with a fork to separate the grains and serve immediately.