Place almonds onto a lined oven tray and into a cold oven set to 200°C. Toast for 10 minutes exactly. Remove and cool slightly.
Place egg whites into Thermomix bowl and whip 5 min/37°C/Butterfly/speed 3/MC off. Remove from bowl and set aside.
Place cooled almonds into Thermomix bowl and mill 10 sec/speed 10. Remove from bowl and set aside.
Place the 100g sugar into Thermomix bowl add butter, almond essence and vanilla. Beat 30 sec/speed 4.
Whip 30 sec/Butterfly/speed 3. Scrape down sides of bowl and repeat.
Add egg yolks and beat 30 sec/Butterfly/speed 3. Remove Butterfly.
Add milled almonds and 120g milk and beat 10 sec/speed 5.
Fold egg whites through almond mixture with a spatula by hand.
Stir rum into remaining milk and arrange first layer of biscuits into a foil-lined tin 2 biscuits wide by 4 biscuits long. A loaf tin works well for this. Alternatively to make individual round ones, use a flat tray and just make little stacks using round biscuits.
Brush every biscuit with milk/rum mixture as you layer them.
Spread with a generous amount of filling between the layers.
Repeat layers of biscuits brushed with milk mixture, topped with the filling 4–5 times, ending with filling.
Wrap cake(s) and refrigerate 24 hours.
To make frosting, place mascarpone, cream, remaining sugar and vanilla into a clean Thermomix bowl and whip 20-30 sec/Butterfly/speed 4 or until soft peaks form.
Remove cake from tin and turn onto serving plate. Frost completely and garnish however you wish. Refrigerate a further few hours if possible. Slice to serve.