Make the sponge starter: combine the warm water, warm milk, yeast, sugar and flour. Cover with plastic wrap and let sit for 15-20 minutes, until the yeast bubbles and a foamy cap forms.
Meanwhile, beat the softened butter, sugar, three eggs and one egg yolk together until smooth - reserve the egg white for the icing.
Combine the sponge starter with the butter-egg mixture, sift in 300g of flour with a pinch of salt, and knead the dough. Knead for 7-10 minutes, adding the remaining flour gradually without overworking the dough.
Gather the dough into a ball, place it in a bowl greased with vegetable oil, and let it rise in a warm place for 1.5-2 hours.
Prepare the raisins: soak them in boiling water, let them steam, drain, dry, and toss in flour.
Punch down the risen dough, add the raisins and citrus essence, and knead for another 5 minutes.
Divide the dough among pans greased with vegetable oil, filling each no more than 1/3 full.
Cover with a towel and let rise for another hour.
Preheat the oven to 160-180°C and bake the kulichi for 30 minutes.
Check for doneness by the golden cap and a dry skewer.
While the kulichi cool, make the icing: whisk the egg white in a clean, grease-free bowl, gradually adding the powdered sugar, bring it to the right consistency and add the lemon juice at the end. Keep the icing covered with plastic wrap until you use it.
Once the kulichi are completely cool, top with icing and decorate.
Happy Easter, and enjoy!