One of the hardest bits of vegan baking is egg replacement. Eggs are annoyingly important for doing things like holding everything together or making things appropriately fluffy. There are a few good solutions, depending what you have to do. For cookies and breads, I like using flaxseed meal. One tablespoon dissolved in 3 tablespoons of water replaces one egg. Handily you can also get either dark or golden flaxseeds, depending on the color of the thing you’re making.
Another option is to make chia eggs (1 tbsp of chia seeds in 3-4 tbsps water = one regular egg). These have to be used for things that will be OK having chia seeds throughout–so I wouldn’t recommend for your sugar cookies for example–but for things that need proper eggy binding, they really do the trick. Plus chia seeds are conveniently good for you and you get to feel smug about eating something called a superfood.
Easily one of my favorite chia egg recipes of all time are these raspberry chia oat bars from oh she glows (which is also one of my favorite recipe sources of all time). They are ridiculously easy to make, free of any refined sugar, full of chia goodness, and I dare you not to eat the whole pan of them in one weekend. Try them out and wonder why you needed eggs in the first place.