Preheat the oven to 350℉, then grease a 10'' round baking pan with butter. Dust the pan with flour or cocoa powder, tapping out the excess, then line the bottom with a layer of parchment paper. Set aside.
Add the almond flour and finely chopped dark chocolate to the bowl of a food processor and blitz until evenly combined, around 1 minute. A few coarse bits are fine—they will give the cake texture.
Sift the cocoa powder and baking powder into the ground almond mixture, then stir until well incorporated. Set aside.
Using a hand mixer or stand mixer fitted with the whisk attachment, cream together the softened butter and ½ cup of granulated sugar on medium-high speed until light and fluffy, around 4 minutes.
Beat in the vanilla bean paste, almond extract, and rum (if using).
Add in the egg yolks one at a time, beating well after each addition, then mix on medium-high speed until pale and fluffy. Set aside.
In another separate bowl, beat the reserved egg whites and salt with an electric mixer until foamy, around 1 minute.
With the mixer running on high speed, gradually stream in the remaining ½ cup of granulated sugar. Continue to whip the egg whites to stiff peaks until a glossy meringue forms. Do not overmix—when you lift the beater, the meringue should hold a stiff and shiny peak but not look dry or lumpy.
To the bowl of whipped butter and sugar, add one large spoonful of meringue and ⅓ of the dry ingredients, then use a rubber spatula to fold everything together until well combined. Repeat this process twice more until all of the dry ingredients have been added.
Gently fold the remaining meringue into the batter until fully incorporated, being careful not to overmix.
Pour the batter into the prepared pan, then use an offset spatula or knife to smooth the top. Bake for 55 to 60 minutes, until a skewer inserted in the center of the cake comes out clean or with a few moist crumbs. Do not overbake.
Place the cake on a wire rack and allow to cool for 1 hour. Run a knife around the edges of the tin, then carefully turn the cake onto a wire rack to cool completely.
To serve, dust the cake with a generous layer of powdered sugar and cut into slices. If desired, serve with whipped cream, ice cream, fresh fruit, or chocolate sauce. Leftovers can be stored at room temperature for up to 3-4 days or in the freezer for 1 month.