01 - In a large bowl or stand mixer, combine warm milk, yeast, and 1 tablespoon sugar. Let stand 5–10 minutes until foamy.
02 - Add melted butter, remaining sugar, eggs, vanilla, nutmeg, and salt. Mix until incorporated.
03 - Gradually add flour, mixing until a soft, slightly sticky dough forms. Knead 7–10 minutes until smooth and elastic.
04 - Transfer dough to a greased bowl, cover, and let rise in a warm spot until doubled, about 1–1.5 hours.
05 - Beat cream cheese, powdered sugar, and vanilla until smooth and creamy.
06 - Punch down dough and turn onto a lightly floured surface. Roll into a 10x24-inch rectangle.
07 - Spread cream cheese filling in a strip along one long edge, leaving a 1-inch border.
08 - Roll up jelly-roll style to enclose filling. Pinch seam and ends to seal. Shape into a ring and transfer to a parchment-lined baking sheet.
09 - Cover and let rise until puffy, about 45 minutes. Preheat oven to 350°F.
10 - Whisk egg with 1 tablespoon milk and brush evenly over cake surface.
11 - Bake 25–30 minutes until golden. Cool completely on a wire rack.
12 - Whisk powdered sugar, milk, and vanilla until smooth but pourable.
13 - Drizzle icing over cooled cake, then immediately sprinkle with alternating stripes of purple, green, and gold sugars.
14 - Optional: Insert a plastic baby figurine into the cake from underneath before serving.