Melt the butter in a deep skillet with a fitted lid over medium heat.
When the butter is melted, add the broken spaghetti and rice. Cook, stirring constantly, for 2 to 3 minutes, until slightly toasted.
Add the chicken broth and bring to a boil. Reduce the heat to a simmer. Cover and cook for 10 to 12 minutes, until the rice is tender and the broth is absorbed.
Remove from the heat and let sit for 5 minutes, then fluff with a fork.