1. For the crust: Pulse together the ground almonds, confectioners' sugar, brown sugar, cocoa, salt, and baking soda in a food processor. Add the butter and pulse until the dough just begins to come together, but is not sticky or wet, about 10 pulses. Remove the blade and turn the dough out into a 10-inch tart pan with removable bottom. Carefully press the dough evenly into the bottom and up the sides of the pan. Refrigerate at least 15 minutes. Preheat the oven to 400 degrees F.
2. For the filling: Separate the eggs and whip the whites until they just hold stiff peaks. In a separate bowl, cream the butter and sugar. Add the egg yolks one at a time and mix until smooth. Stir in the almonds and melted chocolate. Gently fold in the egg whites. Spoon into the chilled crust.
3. Bake until the chocolate just starts to set, 15 minutes. Press the figs gently into the filling in a circle around the tart and continue baking until slightly puffed and set throughout, 20 to 25 minutes. Cool. Cut and serve with creme fraiche, if desired.
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