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 - Whisk flour, sugar, salt, and nutmeg in a large bowl. Add melted butter, eggs, vanilla, and activated yeast mixture. Stir until combined, 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, draft-free spot for 1-1.5 hours until doubled in size.
04 - Punch down risen dough and turn onto a lightly floured surface. Roll into a 10x20-inch rectangle.
05 - Brush melted butter evenly over the rolled dough. Mix brown sugar and cinnamon, then sprinkle mixture uniformly over the buttered surface.
06 - Starting from the long edge, roll the dough tightly into a log. Pinch the seam firmly to seal.
07 - Shape the log into a ring and transfer to a parchment-lined baking sheet. Pinch the ends together securely to seal the circle.
08 - Cover loosely and let rise 45-60 minutes until puffy and slightly increased in size.
09 - Preheat oven to 350°F. Bake for 25-30 minutes until golden brown and cooked through. Cool completely on a wire rack.
10 - Whisk powdered sugar, milk, and vanilla extract until smooth and pourable. Adjust consistency with additional milk if needed.
11 - Drizzle icing evenly over the cooled cake. Immediately sprinkle purple, green, and gold sugars in alternating bands while icing is still wet.
12 - Optionally insert a plastic baby figurine from underneath after baking and cooling. Ensure guests are aware of the hidden tradition.