01 - Combine warm milk, yeast, and 1 tablespoon sugar in a large bowl or stand mixer. Let stand 5 to 10 minutes until mixture becomes foamy and active.
02 - Add melted butter, remaining sugar, eggs, vanilla, nutmeg, and salt. Mix until fully incorporated.
03 - Gradually incorporate flour, mixing until a soft, slightly sticky dough forms. Knead 7 to 10 minutes until smooth and elastic.
04 - Transfer dough to a greased bowl, cover with plastic wrap or damp towel, and let rise in a warm draft-free spot until doubled in volume, 1 to 1.5 hours.
05 - Beat cream cheese, powdered sugar, and vanilla until completely smooth and creamy. Set aside.
06 - Punch down risen dough and turn onto a lightly floured surface. Roll into a 10 by 24 inch rectangle.
07 - Spread cream cheese mixture in a strip along one long edge, maintaining a 1-inch clean border.
08 - Roll dough jelly-roll style to enclose filling. Pinch seam and ends firmly 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 during final 15 minutes of rising.
10 - Whisk egg with milk and brush evenly over entire surface of the cake.
11 - Bake 25 to 30 minutes until deep golden brown. Transfer to a wire rack to cool completely.
12 - Whisk powdered sugar, milk, and vanilla until smooth and pourable. Adjust consistency with additional milk if needed.
13 - Drizzle icing over cooled cake. Immediately sprinkle with alternating stripes of purple, green, and gold sanding sugar.
14 - Optional: Insert a plastic baby figurine into the underside of the cake before serving.