Melt the butter in a large skillet over medium-low heat.
Add the orzo 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.
Add the minced garlic and cook about 1 minute until fragrant, stirring to prevent burning.
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, and simmer until the rice is tender and liquid is absorbed, about 20 to 25 minutes.
Remove from heat and let stand, covered, for 5 minutes.
Fluff the pilaf with a fork to separate the grains and serve immediately.