Line or grease an 8 or 9-inch round springform pan. Preheat the oven to 350F (180C).
In a small bowl, add the butter, cut into pieces, and the chocolate. Melt in a double boiler or in the microwave for 45 seconds (80% power), adding 20 more seconds as needed. Whisk until smooth, and set aside to cool.
In a large bowl, beat the egg yolks with the powdered sugar until light and foamy. Save the egg whites in a separate large bowl for later. Add the vanilla paste (or extract) and the rum. Mix some more.
Add the melted butter/chocolate and beat some more. Add the almond flour and baking powder, and mix until combined.
Beat the egg whites in a separate bowl until firm. Fold into the cake batter.
Pour into the prepared pan, level, and bake for 35 to 40 minutes golden and set. Test with a toothpick for readiness. Let cool, remove from the pan and serve with powdered sugar.
