Combine the chicken broth, butter, salt and pepper in a medium saucepan over medium-high heat. Bring to a simmer, cover, then hold at a low simmer over medium-low heat.
Meanwhile, heat the olive oil over medium-low heat in a high-sided, lidded saute pan. Add the vermicelli and cook, stirring constantly, until golden brown all over, 5 to 6 minutes. Add the rice and cook, stirring, until the grains turn from pale white to bright white, 5 to 7 minutes.
Carefully pour the simmering broth mixture over the rice and vermicelli. Scrape down the sides of the pan, making sure that all of the rice is submerged in broth. Bring to a low simmer, cover and cook for 15 minutes. Remove the lid and continue cooking until all of the liquid is absorbed, about 5 more minutes.
Add the parsley and fluff the pilaf with a fork. Season with salt and pepper. Transfer to a serving dish and serve hot.