Melt butter in sauce pan. Brown egg noodles in butter. Keep stirring and be careful not to burn them or the butter. If you look away to see what Phineas & Ferb are doing, for even a second, they will burn. I've warned you.
As soon as the egg noodles start to brown, add broth and water. Bring to boil. Add rice. Boil for 1 minute. Then lower heat and simmer rice, covered, for 20-25 minutes.
*You can pull this off with brown rice, but add a little bit more water and a little bit more cooking time - maybe 10 minutes.