Preheat the oven to 350°F (180°C) and butter and line with parchment a 9-inch (23 cm) springform pan. Set aside.
Melt the chocolate either in the top of a double boiler over simmering water or gently in the microwave. Set aside to let cool.
In the bowl of a stand mixer fitted with a whisk attachment, whip the butter, salt and ½ cup (4 oz/115 g) sugar on medium-high until pale and fluffy, about 3 minutes.
Whip in the vanilla extract and then the egg yolks, one at a time, scraping down the sides of the bowl every now and then to ensure even mixing. Stir in the melted chocolate until combined.
Transfer the mixture to a large, clean bowl and thoroughly wash and dry the mixer bowl and whisk.
Reattach the whisk and add the egg whites to the clean mixer bowl. Whip on high until soft peaks form, about 3 minutes. Gradually add the remaining ½ cup (4 oz/115 g) sugar and continue to beat to stiff, glossy peaks, a further 3-4 minutes.
With a metal spoon, gently fold in ⅓ of the whipped egg whites into the chocolate mixture to lighten the batter before folding in the remaining whites.
Lastly add the cake flour in 2 additions, mixing just until combined.
Spread the batter into your prepared pan and bake for 50-55 minutes, until a cake tester inserted in the middle comes out clean.
Let cool for 10 minutes before releasing the sides and let cool completely.
Combine the jam and rum in a small saucepan and warm over medium heat, stirring constantly for about 2 minutes, until the jam is runny. Press through a fine mesh strainer and discard the solids.
Transfer the cake to a wire rack set over a rimmed baking dish. Level the top if it is domed, then split the cake in half.
Spread ½ of the jam on the bottom half of the cake then place on the top layer. Brush the top and sides of the cake all over with the remaining jam and let this set and dry, about 30 minutes.
Place the chocolate and butter in a small saucepan over low heat and warm, stirring frequently, until the butter and chocolate is melted and smooth.
Starting in the center of the cake, pour the chocolate in a circular motion over the top of the cake and let it drip down the sides. Tilt the wire rack a bit to encourage even spreading. If needed, use an offset spatula to smooth the sides. Let the glaze set until dry, for about 1 hour.
Using an offset spatula, gently loosen the cake from the wire rack and transfer to a serving dish.
If you wish to add decorations or the word ‘Sacher’ to the top of the cake, scrape the collected glaze from the pan below the rack into a small pan and warm until softened enough to pipe. Strain to remove any cake crumbs, then place the glaze in a small piping bag fitted with a small round tip and write ‘Sacher’ over the top of the cake (or add whatever designs you wish). Allow to set before serving.
Serve slices of cake with freshly whipped cream. Store the leftover cake covered, at room temperature for up to 3 days.