Add the raisins and rum into a small bowl. Stir the raising with rum for a minute so they absorb as much rum as possible then pour boiling water over to cover the raisins. Set aside.
Add 8 tablespoons butter (115g) into a medium saucepan and heat until melted. Add the cold milk, vanilla extract, and 1/4 cup of sugar (50g, you can just eyeball it), stir until combined, then take the pot off the heat. Pour the mixture into a medium bowl, make sure the temperature of the liquid is between 100-110°F (38-43°C) (pleasantly warm to your finger, it can't be too hot) then stir in the yeast (adding yeast into a warm liquid will make them rise faster). After about 1-2 minutes you should see the yeast is starting to 'bloom' (will be frothy/foamy).
Add the eggs, egg yolks, lemon and orange zest, and the remaining sugar (1/2 cup=100g) into a large bowl. Whisk until well combined. Add the salt, flour, the yeast mixture, and drained raisins.
Stir with a spoon until roughly combined then start kneading by hand or with a stand mixer using a dough hook attachment. Knead the dough until it has come together and it's smooth (for about 7 minutes on speed 2 in KitchenAid), then slowly add the remaining 5 tablespoons of very soft butter. Add one tablespoon and knead the dough until the butter is incorporated, then add another tablespoon and repeat the process (it took me 6 minutes on speed 2 in the Kitchen Aid). If you're kneading the dough by hand, it will take a little bit longer.
The dough will be loose, soft and a little bit sticky. Scrape the dough from the sides of the bowl with a spatula and knead it by hand for a minute. After this time the dough should be smooth, soft, and should no longer stick to your hands (it will be oily and loose). If you have used a kitchen scale to measure out the flour you can trust the recipe and use the exact amount written in the ingredient list but if you’re using measuring cups you have to assess the texture of the dough and add more flour/liquid if necessary.
First rise: Form a smooth dough ball, put it back in the bowl, cover the bowl tightly with plastic foil, and place in a warm place for about 1 3/4 hours or until doubled in volume (I'm putting it in a turned off oven with a light on).
Grease a 10 or 12-cup bundt pan generously with soft butter (I used a 10 cup /25 cm (measured at the top) bundt cake pan).
Second rise: Take the risen dough out of the bowl and knead it for 30 seconds. Stretch the dough into a log then pinch thoroughly both ends together. Place it in the bundt pan. Wrap tightly with plastic foil and let rise for 30-40 minutes or until the dough reaches the top of the pan.
Place the baking rack on the lowest position (the babka will be quite tall). Preheat the oven to 350°F (175°C).
Bake the babka for 40 minutes (if you have used a larger baking pan and your cake is not as tall as mine, you might have to bake it for a shorter period of time).
Invert the cake on a cooling rack and let cool completely (it will take about 45 minutes-1 hour).
When the babka is cooled, make the glaze by whisking powdered sugar with lemon juice and water until thick glaze forms.
Pour the glaze over the babka. Let the glaze set a bit then cut the babka into servings with a serrated knife.