Melt butter in a large saucepan over medium heat. Add pasta and cook, stirring often, until golden brown and very fragrant, about 4 minutes. Add rice and gently stir to coat in butter. Add broth and a big pinch of salt, increase heat to medium-high, and bring to a simmer. Stir once, then cover and reduce heat to low. Cook until broth is absorbed and rice is tender, 18–20 minutes. Remove from heat, uncover, and fluff rice gently with a fork. Cover and let sit 5–10 minutes before serving.