One of my favourite websites for recipes, both sweet and savoury is Madhuram's Eggless Cooking. Anything that isn't fully vegan, or fully wheat free, can be so easily modified that there really isn't any worry about 'cake failure'.
One of the first recipes I tried was this one for eggless brownies, which uses silken tofu as an egg replacer. The original recipe calls for one stick of butter, but I simply replaced that with Pure Soya Spread. I left out the walnuts as well, because I cannot abide walnuts (I know they are jam packed full of essential nutrients, but, to me, they taste like they were forged in Hell).
Not the best pic but they tasted heavenly....
I've since played around with the recipe and found the one that works best for me is when the silken tofu is joined by a couple of ripe bananas to add to the binding process. The bananas are incredibly helpful in ensuring that the brownies don't become too crumbly, making them easier to divide into sections.
Also substituting the vanilla extract for orange extract creates that familiar, and nicely appreciated, dark chocolate-orange combo; which tastes even better when made with this amazing stuff from Hotel Chocolat:
Happy baking :-)