Soak the peas overnight (alternately, you can boil them on the stove for about two hours).
Drain and rinse the peas.
If using corned beef, add it to the pot with just enough water to cover, and boil until the meat is done.
There should be about two cups of water in the pot for the next step, so if you are making this with corned beef you'll need to drain the liquid, reserve and measure it, then add enough water for a total of two cups. If you're making it without the beef just add two cups of fresh water to the beans, then bring to a boil.
Add the rice, lime juice, thyme, hot sauce and butter, then cover and reduce heat.
Simmer until the liquid is absorbed (for about 20 minutes).