Preheat the oven to 180C. Line a 6" square tin with parchment.
In a large bowl, add all the ingredients and give them a good whisk.
Turn batter into the tin and bake for about 30 minutes. Cool completely. Trim the top.
Chocolate layer
Heat the cream to steaming and add the chocolate to it. Leave for 10 minutes until the chocolate softens. Whisk until smooth.
Coffee & vanilla mascarpone layer
Whisk the cream and agar agar in a glass bowl. Microwave for 30 seconds, whisk again. Repeat until the cream begins to thicken at the edges, 2-3 times. Note: You can also make this on the stove top. Make sure to stir constantly.
Add in the white chocolate and leave to stand until the chocolate melts. Whisk until smooth. Whisk in the mascarpone.
Divide the mixture into 2 bowls. Add the coffee powder to one and the scraped vanilla bean to the other.
Snugly fit an acetate sheet around the eggless chocolate sponge. Moisten the cake with Kahlua/shot of coffee.
Layer 1 - Pour the chocolate filling over the cake and place in the freezer until firm on top, 30-45 minutes.
Layer 2 - Pour the coffee filling over the chocolate layer and place in the freezer until firm on top, 30-45 minutes. Place the vanilla filling over warm water in the meantime to stop it from setting.
Layer 3 - Pour the vanilla filling over the coffee layer. Place in the freezer for 3-4 hours until very firm, gently peel off the acetate sheet, then leave to set in the fridge overnight.