Sift together the flour and cornstarch into a small bowl (you can just use a sieve to sift them if you don’t have a flour sifter).
Add one third of the tempered egg yolk mixture to the beaten egg whites in the large bowl and sprinkle with one third of the flour mixture. Use a silicone spatula to fold them gently together. Repeat two more times until the flour and yolks are just incorporated and you have a large bowl of fluffy batter. Don’t over-fold or the batter will deflate, and you want it nice and fluffy.
If you are using apricot jam between the layers (I prefer this, but have made it without and it’s also good), then in a small saucepan on the oven or a bowl in the microwave, heat ½ cup of the apricot jam until it’s melted and have it ready.
If using the 9-inch springform pan, plop a heaped half-cup of batter into the prepared pan. If using the two 8-inch springform pans, plop an even half-cup of batter into each pan. (I like to use a ½-cup dry-measuring cup and a small spatula to scrape out the batter.) Smooth the batter into a thin, even layer with the back of a spoon or a spatula. Place the baking pan (or pans) on the rack under the broiler and grill just until the top is a nice dark golden brown. Watch the pan (or pans) closely. It will only take about 45 to 60 seconds (although the first layer may take a bit longer).
Remove the pan (or pans) from the oven and add another layer of batter. Broil it again. But watch it very carefully – the batter can go from raw to burnt in a matter of seconds! And broilers can cycle on and off the longer they’re in use, to keep their heat even, so some layers may be done much more quickly than others. It needs vigilant watching. You want the layers brown enough to cook the batter fully and to show when slicing the cake, but not so brown they are burnt. Try to make each layer of batter flat and even, spreading it to touch the edges of the pan, so you don’t have a domed or dipped top on your cake when it’s done.
Keep spreading and broiling layers, but if using the apricot jam, brush on a thin layer of jam under the batter about every third layer. If using the 9-inch pan, keep adding the jam layers until you’ve used up the ½ cup of jam you’ve heated. If using two 8-inch pans, use up the jam until you’ve got about 2 tablespoons of it left – you’ll save this to stick the two cakes together when they’re cooled.
If using a 9-inch pan, you should have about 12 layers of batter in total. If using the two 8-inch pans, you should have about 8 layers in each, for 16 total layers. The whole process of broiling the batter layers will take 30 to 45 minutes, depending on if you are using one or two pans.
When you’ve completed the last layer, set the cakes aside to cool completely. Remove the cake pan sides. If using two 8-inch pans, spread the remaining 2 tablespoons of jam (you may have to reheat it) on one cake and stack the other cake on top. At this point you can wrap the cooled cake well with plastic wrap and glaze it the next day, or wrap it and put it into a freezer bag to freeze it for up to 3 months for a future occasion.
To glaze the cake: Heat the remaining ½ cup of apricot jam and mash any large chunks of apricots with a fork. Use a pastry brush to brush a layer of jam all over the top and sides of the Baumkuchen, settling any smallish lumps of apricots into any low spots or dips. Use all the jam. Allow the cake to sit uncovered for about an hour to allow the jam to set and get tacky.
In a small saucepan heat the chocolate, cream, coconut oil, and rum over low heat, stirring often, just until about ¾ of the chocolate bits are melted. Remove from the heat and keep stirring until the remainder of the chocolate is melted and the glaze is smooth and shiny. Allow it to cool for a few minutes, until it thickens slightly to a flowing but spreadable consistency, kind of like a thin pudding.
Set the Baumkuchen, still attached to the base of the springform pan, onto an upturned saucer set onto a piece of wax paper or parchment paper to catch any drips. Pour the glaze in a puddle on the top of the cake, then use a spatula to gently work small amounts to the edge of the cake so they drape down the sides. Using the spatula, spread the glaze over a section of the side. Keep bringing some glaze from the top and spreading it around until the sides are all covered. Then smooth the glaze on the top of the cake. You can let the glaze set and leave the cake as is, or you can add the toasted almonds to the sides. Let the glaze partially set, then pat the almonds onto the sides of the cake, using small amounts in the palm of your hand. Individually pick up any fallen ones and stick them into any bare spots to evenly cover the sides of the cake.
Let the glaze set, then use two flat pancake flippers to carefully slide the cake off the base and onto a serving plate, or just set it onto the serving plate still attached to the springform base. Baumkuchen is nice served with mounds of lightly sweetened whipped cream.
Makes 12 to 16 slices of delicious, show-stopping Baumkuchen.
