Preheat the oven to 325 degrees F. Butter the bottom and sides of a 9-inch springform pan and line the bottom with parchment paper. I used a cake pan with parchment and lifted it out.
Put the chocolate in a heatproof bowl and set over a saucepan of simmering water.
Stir until the chocolate melts, then remove the bowl from the pan.
Mix the sugar with the cinnamon and cayenne pepper. You can start with less of each, and add more at the end as you taste it. See notes.
Put the eggs, sugar and salt in the bowl of a stand mixer. Set the bowl over the same pan of simmering water and whisk until the mixture is warm, about 2 minutes.
Transfer the bowl to the stand mixer; beat with the whisk attachment on medium speed until tripled in volume, about 5 minutes.
Boil beer and vanilla in small saucepan until it reaches a low boil.
Reduce the mixer speed to low; beat in the beer mixture, then the melted chocolate, until combined, about 2 minutes. Gradually beat in the softened butter until incorporated.
Pour the batter into the prepared pan. Bake until a toothpick comes out with a few crumbs, about 35 minutes. Do not overbake.
Cool in the pan on a rack 1 hour, then run a knife around the edge of the pan and remove the ring. Let cool completely.