Melt butter in large saucepan over medium-high heat. Add the egg noodles and stir until they begin to brown, being careful not to burn the butter. Stir in the rice. Continue stirring until rice is coated with butter.
Pour in the chicken broth and add the bouillon cubes. Bring to a boil; reduce heat to low and cover tightly. Cook without uncovering pot until all the liquid has been absorbed, about 20 minutes.