Make the sponge cake
Position a rack in the center of the oven and heat the oven to 350°F. Butter a standard 18 x 13-inch half sheet pan and line with parchment paper.
In a large bowl, beat the egg yolks, 1/3 cup of the sugar, the vanilla, and 2 Tbs. warm water with an electric mixer on high until thickened and very pale yellow, 5 to 6 minutes.
In a stand mixer fitted with a whisk, beat the egg whites on medium speed to soft peaks. Gradually pour in the remaining 1/3 cup sugar. Raise the speed to medium-high and continue beating until glossy stiff peaks form.
Fold a third of the egg whites into the yolk mixture to lighten, and then gently fold in the remaining whites. Sift the flour and salt over the top of the mixture and gently fold it in. Pour the batter into the prepared pan, gently spreading and smoothing it to make sure it’s level. Bake until the top springs back lightly when touched, 10 to 12 minutes. Transfer to a wire rack and let cool completely.
Make the chocolate mousse:
Melt the chocolate with the butter in a medium heatproof bowl over a pan of barely simmering water. Set aside.
In a stand mixer with the whisk attachment, beat the egg whites on medium speed until soft peaks form, 2 to 3 minutes. Gradually pour in the sugar, raise the speed to medium-high, and continue beating until glossy stiff peaks form.
Put the heavy cream in a large bowl and beat with a handheld mixer on medium speed until medium-stiff peaks form, 2 to 3 minutes.
Whisk a spoonful of the whipped cream into the melted chocolate. With a rubber spatula, fold in the remaining whipped cream and then the egg whites. Transfer to a pastry bag fitted with a star tip and refrigerate.
Make the candied orange peel:
With a sharp paring knife, cut the orange peel away from the flesh into 2-inch-thick strips. Remove almost all of the white pith from the peel (leaving about 1/8 inch of the pith intact). Cut the peel lengthwise into 1/4-inch strips (you should have about 1/2 cup of peel).
Fill a 2-quart saucepan three-quarters of the way with water and bring to a boil over high heat. Add the orange peel and cook to remove some of the bitterness, 4 to 5 minutes. Drain the peel, run under cold water, and drain again.
In the same pan, add 1/2 cup of the sugar and 1/4 cup of water; bring to a boil over medium-high heat. Add the orange peel, reduce the heat to maintain a very gentle simmer, and cook until the peel is translucent, 20 to 25 minutes. Drain the peel.
Set a rack over a baking sheet lined with parchment paper. Put the remaining 1/4 cup of sugar in a bowl. Toss the peel in the sugar, in batches, and then shake in a sieve to remove any excess sugar. Arrange the orange peel on the rack and leave to dry, 3 to 4 hours.
Make the ricotta cream:
In a large bowl, mix together the ricotta, sugar, lemon zest, and orange zest until combined.
Cut the sponge cake into 1/2-inch cubes. In a small bowl, mix the rum with 1 Tbs. of water. Divide the cake among six 4-ounce glasses. Brush the cake cubes with a little of the rum mixture. Pipe the chocolate mousse over the sponge cake. Divide the ricotta cream among the cups. Sprinkle each cup with the almonds and pistachio nuts and then top with the candied orange peel.