If you can find fine egg noodles, use those instead of the angel hair pasta. To break pasta into small pieces without making a mess, hold them inside a paper bag as you break them apart.
Combine in a large, wide saucepan or deep skillet over medium heat and stir until the noodles are toasted and brown:
Add and cook, stirring, until the rice is translucent around the edges:
Add and bring to a boil:
Reduce the heat to low, cover, and simmer gently for 20 minutes. Allow to stand off the heat, covered, 5 minutes before serving. Fluff with a fork.