Aquafaba: This is the liquid from a can of cooked beans. I tested these brownies with the liquid from can of chickpeas and black beans (Sainsbury's own brand). Both worked great. I like to make sure I shake the can a lot before I open it & drain off the aquafaba which helps to dislodge the sediment from the bottom of the can (which I believe helps the aquafaba to whip up more reliably). If your aquafaba isn't whisking up properly, try reducing it over a low heat until halved in volume before measuring and using in the recipe. Also, note that aquafaba definitely takes longer to whisk into a stiff foam than egg whites do, so give it some time!!! A stand mixer is the best option here as the extra power makes it whip up in no time whereas my experience using hand-held whisks is that it takes longer to reach the right consistency.
Cream of tartar: I add this to help stabilise the aquafaba foam which, in the end, leads to slightly less sunken brownies. However, I've tested it multiple times without COT and they're just as good, probably just a bit fudgier in the end.
Caster/ superfine sugar: golden caster sugar works here as well as white caster sugar. If you can't get this, try blitzing granulated sugar in a food processor or blender until fine (let it settle before removing the lid!). Likewise, powdered sugar (icing sugar) works - just make sure you're using the same weight (so if you're measuring by volume you'll need to adjust the number of cups). Otherwise, just use granulated sugar - this means you'll probably have to whip the mixture for longer and you may not get as fine a texture.
Vegan butter: I used Naturli vegan block (from Sainsbury's in the UK) which is a solid block 'butter' with a fat content of 75%. DO NOT use a low fat margarine here!
Vegan dark chocolate: I used a Guittard 70% chocolate here but Pico is also a great brand of vegan chocolate to use. Otherwise, check the packet of your chocolate to ensure it's vegan - most dark chocolates around 70% cocoa content already are dairy-free.
Sourdough discard: This isn't leavening the brownies so it does not need to be active. I save my discard in the fridge in a lidded container for a week or two and then use it for baking. 100% hydration means that your sourdough is fed with equal weights of water and flour. My sourdough starter is 50:50 rye and white wheat flour but an all white starter, or a 50:50 white/wholemeal wheat flour starter will also work.
Ground Almonds: Other good substitutes are ground hazelnuts or ground cashews. If you can't do nuts, try ground sunflower seeds. You can make your own by pulsing nuts/seeds in a food processor or blender until mealy.
Cornflour: These do work without the cornflour in them but they will be a bit softer and more fragile. The cornstarch just helps bind things together a bit better but if you don't have any, they will still work out.
No sieve: instead, combine the cocoa powder, ground almonds, cornflour, bicarb and salt in a small bowl. Stir together with a whisk or a fork to remove any lumps.