Maybe you can eat eggs just fine but you’ve simply run out of farm fresh eggs temporarily and don’t want to run to the store and pay insane prices for inferior quality organic eggs.
Some folks use a few ounces of applesauce or a mashed up half banana as a substitute for one egg, but in my experience, the binding ability of fruit is not that great. It can also unexpectedly change the taste of the recipe which may not be desirable.
Here’s the substitute I would recommend as it works really well: the gel that you get from soaking flax or chia seeds.
When you soak flax or chia seeds for just a few minutes in plain water (1 TBL seeds soaked in 1/3-1/4 cup of filtered water per egg to be replaced), the soaking water becomes gel-like and can be used as a perfect substitute for eggs in all your favorite recipes.
You can even whip the flax (or chia) gel to get an even lighter and fluffier end result!
* Note that if you have any thyroid issues, it is best to use chia seeds as flax is a slightly goitrogenic food.
Those who live in France should use chia seeds as flax has been banned for human consumption since 1973 and has limited availability in other European countries like Germany, Belgium and Switzerland. To my knowledge, this ban is still in effect at the present time.
Below is a short, 2 minute video which demonstrates the process in my kitchen.