Preheat the oven to 400 F and line an 11-x-17-inch sheet pan with parchment paper.
Whip the 2 egg yolks and the whole egg with the ¼ cup of sugar until it is thick, pale and holds a ribbon when the beaters are lifted. In a separate bowl, stir the ground almonds and flour together.
In another bowl, whip the 2 egg whites until foamy, then slowly add the remaining 2 Tbsp of sugar, whipping until they hold a soft peak when the beaters are lifted. Fold the whipped whites into the yolks in 2 additions, then fold in the almond mixture. Spread this evenly over the prepared sheet pan, ensuring that the batter is as level as possible (the batter will only make a thin layer). Bake the cake for about 8 minutes, until golden brown and allow to cool. Once cooled, the cake make dry a bit – that is expected.
For the ganache, heat the cream until it just begins to simmer and then pour this over the 8 ounces of chopped chocolate. Let this sit a minute, then gently stir with a spatula starting at the centre and widening the circles until the chocolate has fully melted and the ganache is smooth. Set aside to cool to room temperature.
For the buttercream, place the egg whites in a bowl and whip with the 2 Tbsp of sugar until just past foamy. Place the remaining ½ cup of sugar in a small pot with 2 Tbsp of water and bring to a full boil over high heat, boiling until the sugar hits 240 F on a candy thermometer. With the mixer on medium speed, carefully add the hot sugar to the whipped whites by pouring it down the side of the bowl (this helps to avoid splashing), then increase the speed and whip until the whites have cooled to room temperature, about 4 minutes. While beating, add the butter a few pieces at a time until combined. While adding the butter, if it appears that the buttercream is not fluffy, or seems curdled, not to worry - simply keep adding the butter, continue to beat and it will come together. There is no risk of overbeating. Add the coffee extract (or espresso) and the vanilla and use at room temperature.
For the coffee syrup, stir the coffee and sugar together until the sugar dissolves.
For the assembly, remove the sheet of cake and cut into three rectangles (about 6-x-11-inches). Brush the bottom of one of the layers with the melted coating chocolate and let this set until firm (or chill 3 minutes). Place this layer, chocolate-side down onto a flat cake board or platter. Brush the layer with coffee syrup, then spread half of the butter cream on top. Top this with a second cake layer, brush it with syrup and now spread two thirds of the cooled (but still spreadable) ganache layer over the cake. Place the final cake layer over the ganache, brush it with syrup and spread the remaining half of the butter cream on top (or you can save about 1/4 cup for garnish).
For the ganache glaze, re-warm the remaining one third of the ganache, adding the coating chocolate and vegetable oil, stirring until smooth. Spread this over the top of the cake (but not the sides), and chill until set, about 2 hours.
Before serving, trim the sides away to reveal clean layers, then slice into 6 rectangle portions (a hot, dry knife makes this easy). If you wish, pipe a little coffee buttercream on top of each and place a coffee bean on top.