For the Cake:
4 oz. (1/2 cup) unsalted butter; more for the pan
3-1/2 oz. (1 cup) cake flour
1 cup plus 2 Tbs. granulated sugar
2 oz. (2/3 cup) Dutch-processed cocoa powder
1 tsp. baking soda
1/2 tsp. baking powder
1/2 tsp. table salt
1/2 cup hot freshly brewed coffee
1/2 cup buttermilk
1 large egg
1 large egg yolk
For the Mousse:
3 oz. bittersweet chocolate, coarsely chopped
3 oz. milk chocolate, coarsely chopped
2 large egg yolks
1/2 Tbs. Lyle’s Golden Syrup, honey, or light corn syrup
2 large egg whites
3/4 cup heavy cream
For the Streusel
6 oz. (3/4 cup) unsalted butter, softened
1/2 cup granulated sugar
1 tsp. pure vanilla extract
5 oz. (1 cup plus 2 Tbs.) unbleached all-purpose flour
2-1/2 oz. (3/4 cup) Dutch-processed cocoa powder
1-1/2 oz. cocoa nibs (about 1/3 cup)
3/4 tsp. fine sea salt
For the Sauce
8 oz. bittersweet chocolate, finely chopped
2/3 cup heavy cream
2 Tbs. Lyle’s Golden Syrup or light corn syrup
Pinch kosher salt
2 Tbs. dark rum
Make the Cake
Position a rack in the center of the oven and heat the oven to 325°F. Butter an 8x8x2-inch square cake pan, line the bottom with parchment, and butter the parchment.
Sift the cake flour, sugar, cocoa powder, baking soda, baking powder, and salt onto a piece of parchment. In a small saucepan, combine the butter and the coffee over medium heat to melt the butter. Transfer to a medium bowl. Whisk in the buttermilk, egg, and yolk and then the flour mixture until incorporated.
Pour the batter into the prepared cake pan and bake until a toothpick inserted in the center comes out clean, about 50 minutes. Cool on a rack for 15 minutes. Invert onto the rack, remove the parchment, and cool completely.
Make the Mousse
Melt the bittersweet and milk chocolates in a medium heatproof bowl over a pan of barely simmering water. Set aside.
In another medium bowl, whisk the yolks and the syrup over the water bath just until warm. Remove from the heat and whisk briefly to cool.
With an electric hand mixer on medium speed, whip the egg whites in a medium bowl until stiff peaks form, 1 to 2 minutes.
With the mixer on medium-high speed, whip the cream in another medium bowl until soft peaks form.
Whisk the yolk mixture into the melted chocolate. Whisk in a spoonful of the whipped cream. With a rubber spatula fold in the remaining whipped cream and then the egg whites. Refrigerate. (The mousse can be made up to 4 hours ahead.)
Make the Streusel
In a stand mixer fitted with the paddle attachment, beat the butter and sugar on medium-high speed until light and fluffy, 3 to 4 minutes. Reduce the speed to low and add the vanilla.
In a medium bowl, stir the flour and cocoa powder. With the mixer running on low speed, add the flour mixture in three increments, including the cocoa nibs and salt with the final addition. Mix until the dough comes together. (The dough can be refrigerated for a week or frozen for up to 2 months.)
Line a rimmed baking sheet with parchment and press the dough into the pan in a 1/4-inch-thick layer.
Bake at 325°F for 8 minutes and then rake with a fork to break into medium clumps. Bake for 7 minutes more and rake again to create small pieces. The streusel will look sandy and will crisp as it cools. (The streusel can be made 1 day ahead.)
Make the Sauce
Put the chocolate in a medium bowl. Put the cream, syrup, salt, and 1/4 cup water in a small saucepan and bring to a boil over medium-high heat. Remove from the heat, pour over the chocolate, and stir to melt.
Assemble
Divide the warm chocolate sauce among twelve 8-oz. glasses. Cut the cake into 1-inch cubes and put 4 in each glass. Drizzle 1/2 tsp. of the rum on the cake cubes. Scoop a spoonful of mousse into each glass. Sprinkle about 2 Tbs. of streusel on top of the mousse, and serve.