Bloom the yeast: In a small bowl, combine the warmed milk with 1 tablespoon sugar and the yeast. Let sit 5 to 10 minutes until foamy and fragrant.

Make the dough: In a stand mixer bowl, whisk together 2 cups flour, remaining sugar, and salt. Add eggs, vanilla, softened butter, and the yeast mixture. Mix with the dough hook on low until combined.

Knead to soft dough: Gradually add remaining flour until the dough is soft, slightly sticky, and pulls away from the bowl. Knead 6 to 8 minutes until smooth and elastic—the dough should pass a gentle windowpane test.

First rise: Place dough in a lightly oiled bowl, cover with plastic wrap or a damp towel, and let rise in a warm spot until doubled, about 60 minutes.

Prepare filling: Beat together softened butter, brown sugar, cinnamon, and nutmeg until spreadable and pillowy.

Shape the cake: Punch down dough, turn onto a lightly floured surface, and roll into a 12 by 18-inch rectangle. Spread the cinnamon filling evenly, leaving a 1/2-inch border. Roll tightly from the long edge into a log.

Form the ring: Pinch seams closed, form a ring, and tuck ends to join. Transfer to a parchment-lined baking sheet.

Second rise: Cover and let rise 30 to 45 minutes until puffed and slightly puffy to the touch.

Bake: Preheat oven to 350°F (175°C). Brush with beaten egg for a glossy finish. Bake 25 to 30 minutes until golden brown and the internal temperature reaches about 190°F.

Glaze and decorate: Cool the cake for 10 minutes, then drizzle the glaze made from powdered sugar, milk, and vanilla. While the glaze is tacky, sprinkle on purple, green, and gold sugars in sections.

Hide a baby under the cake after cooling or warn guests if inserting before serving.