If undercooked eggs are a concern, you’ll want to make sure you heat the oat bran up to 165 degrees in order to eliminate any salmonella risks with the eggs.
For a protein boost alternative, I also sometimes add collagen protein power to this! (affiliate link)
The longer you keep the oat bran over heat, the more it will thicken and absorb moisture. I often add more water or milk after adding the eggs, right before serving, to make sure it stays creamy and doesn’t get gloppy. The texture reminds me of cream of wheat!
