In a medium saucepan, melt the butter over medium heat. Once melted, add the finely diced onion. Sauté for 3-4 minutes until translucent. Add the minced garlic and cook for 1 more minute.
Add the orzo pasta to the saucepan, stirring for 2-3 minutes to toast it slightly.
Incorporate the uncooked white rice and stir well. Pour in the chicken broth and bring to a boil. Reduce heat to low and cover.
Simmer for 15-20 minutes until the rice is tender and liquid is absorbed. Avoid lifting the lid frequently.
Remove from heat, fluff with a fork, and season with salt and pepper. If desired, sprinkle with fresh parsley before serving.