I have tried a few different egg substitutes. There is powdered egg replacer, which can be bought from health-food shops, it works reasonably well in cookies. For cakes I have used 'flax-eggs' and 'chia-eggs' made by mixing the respective seeds with water until they turn gloopy.
But none of those compare to aquafaba. When I first came across it, I was literally hopping with excitement!
Aquafaba means 'bean-water'. It is the gloopy liquid that you get in a tin of chickpeas, or other canned beans. You'd normally tip it down the sink (I used to). But instead of throwing it away, put it in a bowl and whisk it. It turns into a foam with a consistency just like egg whites. This leads to lots of exciting options that were previously not possible when cooking without eggs: meringues, French macarons and even mayonnaise!
For further info, including the story about how aquafaba was discovered, see the aquafaba website.
For cutting edge recipes, see this facebook group. All of my aquafaba experiments have come from here.
A word of warning... Since aquafaba is made from the liquid surrounding tinned legumes, it is quite likely to be high FODMAP. Proceed with caution if you are following the low-FODMAP diet.
If you are keen to try out aquafaba I recommend you try this first. The recipe is from the Vegan Meringue facebook group:
The basic recipe for aquafaba meringues is aquafaba to sugar somewhere in between 1:2 and 2:1 ratio, with completely optional ingredients to help stiffen the peaks, like vinegar or cream of tartar. You then bake it between 80C/176F to 110C/230F, depending on your oven.
I love French Macarons, with their crispy outer shells and delicious chewy interiors. They are naturally gluten-free since they are made with almond flour. The cream in the middle would not normally be dairy-free but this is easy to fix with dairy-free buttercream. That they can now be made egg-free as well fills me with happiness!
However they can be difficult to make. They are supposed to be smooth on top and have 'feet'. As shown here, I clearly need to work on this!
Recipes and inspiration can be found on the Floral Frosting blog.