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1
For the cake: Preheat the oven to 350F.
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2
Line a 12 by 17-inch rimmed baking sheet with parchment paper and brush the sides of the baking sheet with melted butter.
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3
In a large bowl, sift together the powdered sugar and cocoa powder, then stir in the almond meal.
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4
In an electric stand mixer or in a large bowl with handheld electric beaters, whip the egg whites until frothy, then add a pinch of salt.
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5
Whip the whites to soft peaks, then add the sugar gradually.
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6
Continue whipping until the peaks are firm yet glossy.
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7
Gently fold in one-third of the dry ingredients, then fold in the remainder.
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8
Pour the batter onto the prepared baking sheet and spread evenly.
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9
Bake until the cake springs back when touched, 12 to 15 minutes.
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10
Let cool completely, then place the baking sheet in the freezer until the cake is cold.
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11
For the ice cream: Peel the bananas and mash them roughly with a wooden spoon.
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12
Cover with plastic wrap, pressing the wrap directly against the mashed bananas, and set aside.
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13
In a saucepan, combine 6 tablespoons of the sugar, the lemon juice, and 1/4 cup water.
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14
Cook over medium heat, swirling the pan until the sugar dissolves.
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15
Bring to a boil and cook until the syrup begins to turn a rich caramel color, about 3 minutes.
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16
Once it begins to change color, it darkens quickly, so watch carefully, swirling the pan so the caramel cooks evenly.
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17
Remove the pan from the heat and add the half-and-half and creamcarefully, as they will splatter.
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18
Stir in another 6 tablespoons sugar and return the pan to medium heat.
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19
Bring to a boil, stirring with a wooden spoon to dissolve the caramel.
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20
In a large bowl, whisk together the egg yolks and the remaining 6 tablespoons sugar until thick and pale.
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21
Whisk in about 1 cup of the hot caramel mixture to warm the egg mixture, then pour the combined mixture into the saucepan of caramel and cook, stirring, until it visibly thickens and reaches 178F on an instant-read thermometer.
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22
Pour over the bananas and stir well.
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23
Chill quickly in an ice bath.
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24
When cold, stir in the chocolate chips.
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25
Churn in an ice-cream maker according to the manufacturers instructions.
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26
Transfer to a freezer container and freeze until the ice cream is firm enough to spread without melting.
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27
Take the cake from the freezer.
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28
Put a sheet of parchment paper and a cooling rack on top, then invert the cake.
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29
Remove the baking sheet and top sheet of parchment, and cut the cake in half across the middle of the long side.
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30
Spread one half with ice cream, making an evenly thick layer.
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31
Invert the other half, including the parchment sheet under it, over the ice cream.
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32
Return the cake to the freezer for at least 2 hours.
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33
To serve, take the cake from the freezer and remove the top sheet of parchment.
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34
With a serrated knife, trim the edges of the cake neatly.
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35
Cut the cake in half lengthwise, then cut each half into 5 triangles.
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36
Transfer the triangles to a serving platter, lifting them away from the bottom sheet of parchment.
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37
Serve immediately.
