There seems to be a stomach bug making the rounds here, and the common wisdom is to go with the BRAT diet (Bananas, Rice, Applesauce, and Toast) until it passes.
I'm okay with the bananas, rice, and applesauce, but what about toast, what else could replace it? (How did bread make the cut for stomach soothing anyway since it such a common irritant?)
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Bananas, Rice, And Taters!
Though it's not strictly paleo, I've seen this version discussed and would argue it's a paleo-friendly one.
Rice and potatoes would fall under the "safe starches" of the Jaminets and, more or less, Dr. Kurt Harris and Richard Nikoley.
As for bananas, see the discussion in one of the other answers.
Pumpkin and bone broth sounds good too - but that's the PABB diet!
My favorite replacement for that forth is bone broth mixed with canned pumpkin. Whenever I used to have stomach issues, this helped a lot.
I'd skip the toast and bananas, only because the sugar in the bananas will only feed that yucky bacteria that your gut is trying to rid itself of.
If you're completely emptied out (from both ends) I would make up a batch of chicken broth (not the low sodium kind--if you've been shitting all day your body is most likely deprived of electrolytes and needs the salt). My favorite sick soup is homemade egg drop soup: Bring a couple cups of broth/soup stock to a boil, and beat a couple of eggs in a cup, drizzle the eggs slowly into the boiling broth, and swish it back and forth with a fork until the egg is cooked (only takes a couple of minutes). Adding a dollop of butter to the soup is a good way to get a little fat in your body and add flavor. Unsweetened applesauce would probably be fine but I wouldn't want to overdo it on the fruit. Stay away from juices for the same reason = sugar.
I thought the BRAT diet was essentially based on bland, low in fat, easy to digest foods. Just apply that concept to paleo when you're feeling iffy - steamed, mushy vegetables with a little butter to taste (you might not want as much because fat is harder to digest), boiled eggs, white meat chicken, etc. I personally just wait it out: after a day or two (even half a day) you starve the germs in your system.