I also use flax (ground up with water added) as an egg substitute and that works really well. 

Depending on the recipe, you can get away with using some banana or even a mix of baking soda and vinegar (we've used both, but prefer flax).

Banana or flax would be the healthiest options, in my opinion, and it produces the best results for us.

While not the healthiest option, if you can get some, products like the Ener G Egg Replacer (Amazon link: https://amzn.to/2VnSdzb) can also be used. We haven't tried any commercial products here at home, so I can't how well that would work, but it is a popular one. 

It was pretty darn good! But I'm wondering, when you make a cookie recipe, what egg substitute do you use?

This recipe used a flaxseed "egg." Seems pretty healthy compared to some other egg substitutes I've seen. Are there a bunch of safe egg substitutes that always work for cookies? I'm trying to figure out what the HEALTHIEST ones are.