01 - Combine warm milk and melted butter in a small bowl. Sprinkle yeast over the surface and let stand for 5 minutes until foamy, indicating the yeast is active.
02 - In a large bowl or stand mixer, combine the yeast mixture with granulated sugar, eggs, vanilla extract, and salt. Gradually add flour while mixing until a soft, slightly sticky dough forms.
03 - Turn dough onto a lightly floured surface and knead for 6–8 minutes by hand, or use a dough hook for 5 minutes, until smooth and elastic. The dough should spring back when pressed lightly.
04 - Place dough in a greased bowl, turning to coat all sides. Cover with plastic wrap or a damp towel and let rise in a warm, draft-free area until doubled in bulk, approximately 1 to 1½ hours.
05 - While dough rises, mix brown sugar, cinnamon, flour, and softened butter in a medium bowl until combined into a spreadable paste.
06 - Punch down the risen dough to release air. Roll into a 10x20-inch rectangle on a lightly floured surface. Spread cinnamon filling evenly over the dough, leaving a ½-inch border around edges.
07 - Starting from a long side, roll dough tightly into a log. Pinch seam to seal, then bring ends together to form a ring, pinching firmly to secure the connection.
08 - Transfer ring to a parchment-lined baking sheet. Cover loosely and let rise in a warm place until puffy and noticeably increased in size, about 45 minutes.
09 - Preheat oven to 350°F. Bake for 25–30 minutes until golden brown and an instant-read thermometer inserted into the thickest part registers 190°F. Cool completely on a wire rack.
10 - Whisk powdered sugar with 2 tablespoons milk and vanilla extract until smooth and pourable. Add additional milk 1 teaspoon at a time if needed to reach drizzling consistency.
11 - Drizzle icing evenly over the cooled cake. Immediately sprinkle purple, green, and gold sanding sugars in alternating diagonal stripes while icing remains wet to ensure adhesion.
12 - If using the plastic baby tradition, insert it into the underside of the cooled cake from the bottom, pushing it about halfway through. This ensures it stays hidden during serving.