Ideally you have all ingredients measured and everything prepped (just in case have a bit extra at hand - I find this particularly helpful if you find that your batter is lacking moisture/substance/sweetness/etc, just add a tad more later on); it's important that all ingredients are at room temperature (c. 20-25C) unless your cake recipe specifically states something else;
With a fork crush the chestnuts into fine flower (you can buy them cooked, but they'll taste better if you roast or cook, then peel them yourself);
Butter & dust the cake tin with flour;
Preheat the oven (hot-air c. 170C);

Step 1: Making the Batter

Whisk the butter with about 1/4 of the sugar till it's creamy & fluffy, then add the rum, finely grated lemon peel, and egg yolks and continue whisking till the batter is fluffy;
Whisk egg whites till stiff (adding a few drops lemon juice will ascertain a smooth batter, and reduce chance of over-whisking), then sslowly&gently adding the remaining sugar while continuing to whisk, till the sugar crystals have melted and the batter is completely white and stiff enough that peaks will remain in shape (see pictures) - my grandmother always said to turn the whisking-bowl upside down, only if the batter doesn't change shape or drip has it been whisked long enough!

Step 2: Blend All Ingredients & Bake

Thoroughly Fold-in about 1/4 of the whisked egg whites with the yolk mixture;
then very GENTLY, and bit by bit, add the dry ingredients and the remaining egg whites (this should be in about about 3-4 steps) - it's important to work swiftly but gently to ascertain that the batter remains fluffy, otherwise the cake won't rise...
Pour/scoop the batter evenly into the tin and put into the oven (lower middle tray); do NOT open the oven for the first 20 minutes (or the cake may collapse); usually it'll take 40 minutes to bake - test with a wooden spike: poke the centre of the cake, if no crumbs remain when pulling it out again, the cake is ready, otherwise continue baking in c.5minute increments - another indicator that the cake is ready is that the batter comes off on one or some of the side of the tin - if the oven doesn't heat evenly I'd recommend to turn the cake after about 20-25 minutes.

Step 3: Icing the Cake

Remove the cake from the tin while it's still warm (if it's still attached to the side of the tin loosen it carefully with a thin knife); allow to cool on a griddle covered with a clean tea towel;
When the cake has completely cooled (about 3-6hours) cut horizontally in half (if it's very high in cut into three layers);
Evenly spread plum preserve (this should be smooth without bits, otherwise blend beforehand) - if you like you can add a little rum (or similar) for extra umphhh! Then reassemble the cake and spread preserve on top and sides as well;
Ice the cake with melted chocolate; decorate if desired (in the picture I used white fondant/lemon-sugar icing).
The cake will taste better on the next day, when the aromas have had time to unfold and blend.
I recommend to serve the Chestnut Cake with whipped cream and nice Viennese coffee!
Bon-apetit ;-)