Preheat the oven to 325°F / 160°C (165°C fan-forced).
Line the cupcake pan with cupcake papers.
Chop the bittersweet and unsweetened chocolate and place in a heatproof bowl set over a saucepan of gently simmering water (double boiler). Add the cayenne pepper and cinnamon. (Tip: flavoured bittersweet chocolate, such as chilli or orange-infused, works beautifully here.)
Stir until the chocolate is melted.
In another heatproof bowl, put the eggs, turbinado sugar and salt. Place the bowl on the same double boiler and whisk until the mixture is warm for about 2 to 4 minutes.
Transfer the egg mixture to a stand mixer fitted with the whisk attachment (or use a hand mixer). Whip on medium speed until the mixture has tripled in volume, about 5 minutes. It should be pale, thick, and leave a ribbon trail when the whisk is lifted.
While that is mixing, combine the coconut rum, vanilla, and instant espresso powder in a small saucepan and bring to a low boil.
Decrease the speed of the mixer to low and gradually pour in the rum/coffee mixture in a thin, steady stream.
Then add the melted chocolate mixture and mix on low speed until fully combined, about 2 minutes. Scrape down the sides of the bowl as needed.
Gradually add the butter until all is incorporated.
Scoop batter into the cupcake papers.
Bake at 325°F / 160°C (165°C fan-forced) for about 10 minutes (for mini cupcakes) and 15 minutes (for regular cupcakes). The cupcakes are done when the tops are set and slightly firm to the touch — they will continue to firm up as they cool.
Let cool completely.
Frosting Instructions
Melt chocolate and butter in a microwave-safe bowl in 30-second intervals using a microwave-safe bowl until all melted. Set aside to cool slightly.
Whisk the egg whites, sugar, cream of tartar, salt and 1/3 cup (80ml) of water in a heatproof bowl.
Place bowl over a double boiler beat with a hand mixer on low, then gradually increase speed to form soft peaks. This takes about 5 minutes. The mixture should reach 160°F / 71°C to pasteurise the egg whites.
Remove the bowl from the pan and continue beating until the mixture becomes cool and fluffy.
Fold in vanilla, then the chocolate.
Transfer the frosting to a piping bag fitted with a large round or star tip (or a zip-top bag with one corner snipped off).