01 - Mix warm milk and yeast in a small bowl. Let stand until foamy, approximately 5 minutes.
02 - In a large bowl, whisk together flour, granulated sugar, salt, cinnamon, and nutmeg until well blended.
03 - Pour the yeast mixture into the dry ingredients. Add eggs and softened butter. Mix until a shaggy dough forms.
04 - Turn dough onto a floured surface and knead for 8–10 minutes until smooth, elastic, and no longer sticky.
05 - Place dough in a greased bowl, cover with plastic wrap, and let rise in a warm spot until doubled in bulk, about 1–1½ hours.
06 - Beat cream cheese, powdered sugar, and vanilla extract in a medium bowl until completely smooth and creamy.
07 - Punch down risen dough and roll into a 10x24-inch rectangle. Spread cream cheese filling evenly, leaving a 1-inch border around edges.
08 - Roll dough tightly from the long side into a log. Pinch seam firmly to seal. Form log into a ring, pinching ends together to close. Transfer to a parchment-lined baking sheet.
09 - Cover loosely and let rise for 45 minutes until puffy. Preheat oven to 350°F during the last 15 minutes of rising.
10 - Bake for 25–30 minutes until deep golden brown and cooked through. Cool completely on a wire rack.
11 - Whisk powdered sugar, milk, and vanilla until smooth and drizzling consistency.
12 - Drizzle icing over cooled cake. Immediately sprinkle purple, green, and gold sanding sugar in alternating bands while icing remains wet.