A little bit of egg is okay occasionally. 1 egg lasts my birds about a week. I do occasionally give plain or blueberry pancakes. Once every other month probably as a treat.
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I usually use Harrison's or Momma's Birdie Bread mixes. This website has several different bird bread recipes.
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Easiest is to start with a healthy flour or pellet base (ancient grains are good for this, like spelt, amaranth, etc). Add an egg and some liquid (I like jarred baby food puree for a veggie boost, 1/2 cup liquid to 2 cups of flour or so) until you get a bread dough consistency, then pop it into the oven at 350F for until baked through, about 30 minutes usually.