In a saucepan, melt the butter over a medium heat, being careful to not burn it. Then add the egg noodles and stir them until they brown. Once the egg noodles have browned, stir in the rice to coat it in the butter, to where it looks shiny. Add in the chicken broth and bring to a boil, stirring occasionally to avoid it sticking to the bottom. Once it's at a boil, cover it with a tight fitting lid and bring heat to a low simmer. Let it cook covered for 20 minutes. No peeking! After the 20 minutes, remove the lid and stir to fluff the rice. If there are some crispy pieces along the bottom of the pan, you did it perfectly! Serve and enjoy!