01 - Combine warm milk (110°F) 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 thoroughly. 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, or use a stand mixer with dough hook for 5 minutes, until smooth and elastic.
04 - Place dough in a greased bowl, cover with plastic wrap or towel, and let rise in a warm, draft-free place until doubled in bulk, approximately 1 to 1½ hours.
05 - While dough rises, combine brown sugar, ground 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 the long side, roll dough tightly into a log. Pinch seam to seal, then form into a ring by connecting ends and pinching together securely.
08 - Transfer ring to a parchment-lined baking sheet. Cover loosely and let rise until puffy and visibly 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 together powdered sugar, 2-3 tablespoons milk, and vanilla extract until smooth and pourable. Add additional milk 1 teaspoon at a time if too thick.
11 - Drizzle icing evenly over cooled cake. Immediately sprinkle purple, green, and gold sanding sugars in alternating diagonal stripes while icing is wet.
12 - Once completely cooled, optionally insert plastic baby figurine into the cake from underneath through a small slit in the bottom.