Preheat the oven to 180 degrees Celsius or 320 Fahrenheit.
Brown the butter in a small saucepan until it reaches a deep golden colour and has a very nutty fragrance. It should weigh 40g or close to that number after browning.
Half fill the small saucepan you used for the brown butter with water and place it on a medium heat. Pour the browned butter into a metal or heatproof bowl and place it on top of the saucepan, ensuring the water doesn’t touch the bottom of the bowl.
Add the chocolate to the saucepan and stir intermittently until it is completely melted. Remove from the heat and set aside.
While the chocolate is melting, add the caster sugar and egg to the bowl of the kitchen mixer. Using the whisk attachment, beat for 7-10 minutes on a medium-high speed until light and kind of fluffy. This helps create lift and a shiny meringue-like top.
While this is happening, whisk together the cocoa, tapioca flour, baking powder and salt in a small bowl.
Once the egg mixture is sufficiently lightened in colour, lower the speed of the mixer and pour in the sourdough starter. Once incorporated, add the melted chocolate. Use a spatula to get every last bit, and allow to continue processing on low until combined.
Spoon in the flour mixture, letting each spoon mix in before adding more. Stop and scrape down the sides of the bowl with a spatula as necessary.
Once the flour has been incorporated, turn the mixer off briefly to add the (optional) vanilla bean paste. If you don’t turn it off, the vanilla paste tends to get tangled in the whisk attachment. Continue mixing until combined.
The batter should fall off the whisk attachment in relatively thick ribbons. It is thick, but still slightly thinner than a traditional cookie dough – you’ll need to use spoons to assemble.