01 - Combine warm milk, warm water, a pinch of sugar, and yeast in a small bowl. Let stand 5-10 minutes until foamy and activated.
02 - Mix flour, sugar, salt, and nutmeg in a large bowl. Add melted butter, eggs, vanilla, and yeast mixture. Stir to combine, then knead by hand or with a stand mixer for 7-10 minutes until smooth and elastic.
03 - Place dough in a greased bowl, cover with plastic wrap or a damp towel, and let rise in a warm spot for 1-1.5 hours or until doubled in size.
04 - Punch down dough and turn onto a lightly floured surface. Roll into a 10x20-inch rectangle. Brush melted butter over dough surface. Mix brown sugar and cinnamon, then sprinkle evenly over buttered dough.
05 - Starting from the long edge, roll up dough tightly into a log. Pinch seam to seal. Shape log into a ring and transfer to a parchment-lined baking sheet. Pinch ends together to seal the circle completely.
06 - Cover loosely with plastic wrap or towel and let rise 45-60 minutes until puffy and noticeably expanded.
07 - Preheat oven to 350°F. Bake cake for 25-30 minutes until golden brown and internal temperature reaches 190°F. Cool completely on a wire rack.
08 - Whisk powdered sugar, milk, and vanilla in a small bowl until smooth and pourable. Adjust consistency with additional milk if needed.
09 - Drizzle icing evenly over cooled cake. Immediately sprinkle colored sugars in alternating purple, green, and gold bands while icing is still wet to ensure adhesion.
10 - Optionally insert a plastic baby figurine from underneath after baking and cooling. Ensure guests are warned about the hidden surprise.