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Place the figs in a blender or food processor with the vanilla extract and the cognac and blend until pureed. You might need to smoosh the unpureed figs down towards to blades in between blending sessions since the mixture will be so thick and sticky (this means you should only do this when the blender is off, don’t want to mix any fingers in with those figs!). Once all of the figs are pureed, remove the thick paste from the food processor and set it on a flat, clean surface (large plate or cutting board will work great). Knead in the chopped dates and sea salt. Once they’re fully incorporated, knead in the sliced almonds and set aside.
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Place a large sheet of plastic wrap over an 8-inch cake pan. Place the cake mixture in the cake pan on top of the plastic wrap and press down until the cake mixture is molded into the shape of the cake pan. Then, try to make the exposed surface as flat as possible, (since this will end up being the bottom of the cake, you want it to be nice and even so it doesn’t end up lopsided when you flip it over the next day).
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Place the pan in the refrigerator and allow it to sit there overnight, do not cover the exposed end as you want the cake to dry out a bit.
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The next day take the cake out of the refrigerator and remove it from the pan by gently pulling up on the plastic wrap. Flip the cake over onto a serving plate so that the exposed side is on the plate and the plastic-wrapped side is facing up. Peel the plastic wrap off the cake and discard the wrap. Decorate the outside of the cake with the sliced almonds, allow to warm to room temperature, and serve.