01 - Combine warm milk, yeast, and 1 tablespoon sugar in a large bowl or stand mixer. Let stand for 5-10 minutes until mixture becomes foamy.
02 - Add melted butter, remaining sugar, eggs, vanilla, nutmeg, and salt to the yeast mixture. Mix until thoroughly combined.
03 - Gradually incorporate flour, mixing until a soft, slightly sticky dough forms. Knead for 7-10 minutes until dough becomes smooth and elastic.
04 - Place dough in a greased bowl, cover with plastic wrap or towel, and let rise in a warm draft-free area until doubled in volume, approximately 1 to 1.5 hours.
05 - While dough rises, beat cream cheese, powdered sugar, and vanilla extract until smooth and creamy. Set aside until ready to use.
06 - Punch down risen dough and transfer to a lightly floured surface. Roll into a 10x24-inch rectangle.
07 - Spread cream cheese filling in a strip along one long edge of the dough, leaving a 1-inch border around the edges.
08 - Roll dough jelly-roll style, enclosing the filling. Pinch seam and ends tightly to seal. Shape into a ring and transfer to a parchment-lined baking sheet.
09 - Cover loosely and let rise until puffy, about 45 minutes. Preheat oven to 350°F during the final 15 minutes of rising.
10 - Whisk egg with 1 tablespoon milk. Brush entire surface of cake evenly with egg wash mixture.
11 - Bake for 25-30 minutes or until golden brown and cooked through. Transfer to wire rack and cool completely.
12 - Whisk powdered sugar, milk, and vanilla extract until smooth but pourable consistency is achieved.
13 - Drizzle icing evenly over cooled cake. Immediately sprinkle alternating stripes of purple, green, and gold sanding sugars over icing while wet.
14 - If desired, insert plastic baby figurine into the cake from underneath before serving.