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First, make the sponge. Put the dried figs in a bowl and pour over the coffee. Leave to soak for 30 mins. Heat oven to 180C/160C fan/gas 4. Tip the hazelnuts onto a baking tray and toast in the oven for 5-8 mins until golden brown and aromatic. Tip 75g of the nuts into a food processor (set aside the rest for later) and leave to cool for 10 mins. Meanwhile grease the base and sides of a 20 x 30cm rectangular cake tin with butter and line with baking parchment.
Whizz the cooled nuts until finely chopped. Add the soaked figs and any remaining coffee, and whizz again to a paste. Add the remaining sponge ingredients to the processor with a good pinch of salt. Blend until well combined, scraping down the sides once or twice and blending again. Scrape into your cake tin, level the surface and bake for 25 mins, or until a skewer inserted into the centre of the cake comes out clean. Cool in the tin for 10 mins, then flip onto a wire rack, peel off the parchment and leave to cool.
While the cake cools, make the icing. Put the butter, vanilla and half the sugar in a large bowl. Roughly mash together with a spatula, then blend with an electric hand whisk until smooth. Add the cream cheese and the remaining icing sugar, mash, then blend again until smooth. Split the icing into 2 batches, one for layering and a crumb coat, and one for a final coat. You can chill the icing while the cake cools, but remove it from the fridge 15 mins before using to bring back to room temperature.
Now assemble the cake. Transfer the cooled cake to a chopping board. Score the sponge at 10cm intervals along the length of the cake, marking out 3 sections, 20 x 10cm each. Cut through, then stack the cakes on top of each other to check they are the same size. Trim any uneven edges, then unstack.
Put 1 sponge on a cake board or plate. Spread with a little icing and 3 tbsp fig jam, keeping the jam about 1cm from the edges. Top with another sponge, more icing and jam, then sandwich with the final sponge. Use a palette knife to cover the entire cake with the remaining first batch of icing (the crumb coat) – don’t worry if it’s a little messy. Make sure you fill any gaps between the layers with icing. Once covered, chill for at least 30 mins to firm up the icing. Chill the remaining icing too, but bring it out of the fridge 10-15 mins before the cake so it is ready for spreading.
Decorate the cake. Remove it from the fridge and cover with the remaining icing. Use a palette knife to create smooth edges, or leave it fairly rough, if you like. Top the cake with the figs, pointy ends up. Put the caramel in a small piping bag, snip off the corner and drizzle over the top of the cake, encouraging it down the sides (or just drizzle it over with a spoon). Roughly chop the remaining toasted nuts and scatter over the top. Serve in slices with extra figs on the side, if you like. Keep leftovers in the fridge for 3 days, but bring to room temperature before eating.