01 - Combine warm milk and melted butter in a small bowl. Sprinkle yeast over the surface and let stand for 5 minutes until foamy and activated.
02 - In a large bowl or stand mixer, combine the yeast mixture, granulated sugar, eggs, vanilla extract, and salt. Mix until blended. Gradually add flour, mixing until a soft, slightly sticky dough forms.
03 - Turn dough onto a lightly floured surface and knead for 6-8 minutes until smooth and elastic. Alternatively, use a stand mixer with dough hook for 5 minutes.
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 1½ hours.
05 - While dough rises, combine brown sugar, cinnamon, flour, and softened butter in a medium bowl. Mix until a spreadable paste forms.
06 - Punch down risen dough and roll into a 10x20-inch rectangle on a lightly floured surface. Spread cinnamon filling evenly over surface, leaving a ½-inch border around edges.
07 - Starting from a long side, roll dough tightly into a log. Pinch seam to seal. Shape into a ring by bringing ends together and pinching to join securely.
08 - Transfer cake to a parchment-lined baking sheet. Cover loosely and let rise until puffy and slightly expanded, about 45 minutes.
09 - Preheat oven to 350°F. Bake for 25-30 minutes until golden brown and cooked through. Cool completely on a wire rack before icing.
10 - Whisk powdered sugar, 2 tablespoons milk, and vanilla extract until smooth and pourable. Add additional milk if needed to reach desired consistency.
11 - Drizzle icing evenly over cooled cake. Immediately sprinkle purple, green, and gold sanding sugars in alternating diagonal stripes while icing is wet.
12 - If using traditional plastic baby, insert it into the underside of the cooled cake before serving. The person who finds the baby in their slice hosts next year's celebration.