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 the 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, and let rise in a warm spot for 1-1.5 hours until doubled in size.
04 - Punch down dough and turn onto a lightly floured surface. Roll into a 10x20-inch rectangle.
05 - Brush melted butter over the dough surface. Mix brown sugar and cinnamon, then sprinkle evenly over the buttered dough.
06 - Starting from the long edge, roll up 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 ends together to seal the circle completely.
08 - Cover and let rise for 45-60 minutes until puffy and slightly increased in size.
09 - Preheat oven to 350°F. Bake for 25-30 minutes until golden brown. Cool completely on a wire rack.
10 - Whisk powdered sugar, milk, and vanilla until smooth and pourable. Drizzle over the cooled cake.
11 - Immediately sprinkle purple, green, and gold decorating sugars in alternating bands while icing is still wet. Optionally insert a plastic baby figurine from underneath after baking and cooling.