01 - Combine warm milk and yeast in a small bowl. Let stand until foamy, about 5 minutes.
02 - Whisk together flour, sugar, salt, cinnamon, and nutmeg in a large bowl.
03 - Add yeast mixture, eggs, and softened butter to dry ingredients. Mix until dough forms.
04 - Knead on floured surface for 8–10 minutes until smooth and elastic.
05 - Place in greased bowl, cover, and let rise in warm place until doubled, about 1–1½ hours.
06 - Beat cream cheese, powdered sugar, and vanilla until smooth and creamy.
07 - Punch down risen dough and roll into 10x24-inch rectangle.
08 - Spread cream cheese filling evenly over dough, leaving 1-inch border.
09 - Roll tightly from long side into log, pinch seam to seal, then form into ring on parchment-lined baking sheet. Pinch ends together.
10 - Cover and let rise 45 minutes. Preheat oven to 350°F.
11 - Bake 25–30 minutes until golden brown. Cool completely on wire rack.
12 - Whisk powdered sugar, milk, and vanilla until smooth and pourable.
13 - Drizzle icing over cooled cake. Sprinkle colored sugars in alternating sections while icing is wet.