01 - Combine warm milk and melted butter in a small bowl. Sprinkle yeast over the mixture and let stand for 5 minutes until foamy and activated.
02 - In a large bowl or stand mixer, combine the yeast mixture with granulated sugar, eggs, vanilla extract, and salt. Gradually incorporate flour until a soft, slightly sticky dough forms.
03 - Knead dough on a lightly floured surface for 6–8 minutes by hand or 5 minutes with a dough hook until smooth and elastic.
04 - Place dough in a greased bowl, cover with plastic wrap or a clean towel, and let rise in a warm, draft-free area until doubled in volume, approximately 1 to 1½ hours.
05 - While dough rises, whisk together brown sugar, ground cinnamon, flour, and softened butter until a smooth, spreadable paste forms.
06 - Punch down risen dough and roll into a 10x20-inch rectangle. 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, then shape into an oval ring by connecting ends and pinching firmly to secure.
08 - Transfer cake to a parchment-lined baking sheet. Cover loosely and let rise until puffy and 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, milk, and vanilla extract until smooth and pourable. Adjust consistency with additional milk if necessary.
11 - Drizzle icing evenly over cooled cake. Immediately sprinkle purple, green, and gold sanding sugars in alternating diagonal stripes while icing remains wet.
12 - If using, push plastic baby figurine into the underside of the cooled cake before serving.