In a bowl of your stand mixer, mix the flour, yeast, salt and caster sugar. Pour the milk in, add the vanilla bean paste and the eggs. Fitted with either a dough hook or a K-beater, run your mixer for approx 6-8 minutes until the dough forms (it will be thin and sticky).
With the mixer still running, bit by bit, add the slivers of soft butter and keep on mixing until all the butter is incorporated.
Cover the bowl with a damp tea towel or cling film and leave in a warm spot to prove for 1.5-2hours, until the dough doubles in size.
In the meantime, place the sultanas and rum in a small saucepan and heat for a minute. Take the pan off the heat just before the rum boils, cover and leave to soak whilst your dough is proving.
Generously grease your bundt cake tin with butter. Spoon 2 tsp of dried breadcrumbs and swish them around so they stick to the bottom and sides of the tin. Tio out any excess. Place the tin in the fridge (this will solidify the butter and prevent your Easter Bundt Cake from sticking to the tin).
Once doubled in size, place the bowl back in the stand mixer. drain the sultanas and discard the leftover rum. Squeezing any excess rum out of the dried fruit, add them to the dough hand run the mixer on low speed to incorporate the fruit into the dough.
Scrape the Easter Babka dough into the prepared bundt cake . Cover with a damp tea towel or cling film and leave for 1.5 hours to prove again. It should double in size.
Preheat the oven to 180 C. Place the cake in the middle of the oven and bake for 30-35 minutes. The skewer inserted should come out clean.
Once baked leave it in the tin for 10 minutes. Then invert the cake onto a wire rack and leave to cool down completely.
In the meantime, mix the icing sugar with lemon juice to make thin(ish) icing. Spoon the lemon icing all over the Polish Babka and leave for an hour to set before slicing!