Preheat the oven to 180 degrees Celsius or 356 degrees Fahrenheit. Grease and line a 24cm springform tin. Place it on an oven tray – this will help make sure you can evenly lower it in and out of the oven.
Place the butter and chocolate in a medium-large metal bowl over a small pot of water. Turn the heat to medium, and allow the steam to melt the chocolate and butter, stirring intermittently. It should eventually reach a smooth consistency.
Add the coffee, sea salt, vanilla bean paste and caster sugar to the chocolate mixture, and mix well to combine. Turn the heat off and carefully remove the bowl from atop the saucepan. Set aside to cool a little.
Separate the egg yolks and whites in super clean bowls, ensuring no yolk gets into the whites. Whip up the whites using your preferred method (I use a KitchenAid) until they are super fluffy and firm - about 5-10 minutes. When the butter chocolate mixture is cool enough, mix the egg yolks in, stirring thoroughly to combine.
Transfer the chocolate mixture into a large, clean mixing bowl. A little at a time, use a spatula to fold the egg whites through the chocolate mixture. The idea is to create a smooth batter without bashing the air out of the whites. Gently scrape them against the surface of the bowl, and continue to do so until the mixture is mostly smooth, but still fluffy.
Pour the cake batter into the lined springform tin, and place it into the oven. Cook for 50 minutes to an hour, and then remove from the oven.
Allow the cake to cool completely before serving. For best results, allow it to sit in the fridge overnight. Slice with a hot knife – it is very fudgy.