01 - Combine warm water, a pinch of sugar, and yeast in a small bowl. Let stand until foamy, about 5 minutes.
02 - Whisk together milk, eggs, softened butter, sugar, salt, nutmeg, and vanilla in a mixing bowl. Add the foamy yeast mixture.
03 - Gradually add flour, mixing until a soft dough forms. Knead by hand or with a dough hook for 8–10 minutes until smooth and elastic.
04 - Place dough in a greased bowl, cover, and let rise in a warm place until doubled in size, about 1–1.5 hours.
05 - Punch down dough and turn onto a lightly floured surface. Roll into a 10x20 inch rectangle. Mix brown sugar and cinnamon, brush rectangle with melted butter, and sprinkle mixture evenly.
06 - Roll up tightly from the long side to form a log. Pinch seam to seal. Transfer to a parchment-lined baking sheet and shape into a ring, pinching ends together. Optionally hide a plastic baby inside.
07 - Cover and let rise until puffy, about 45 minutes. Preheat oven to 350°F.
08 - Bake 25–30 minutes until golden brown. Cool completely on a wire rack.
09 - Stir powdered sugar, milk, and vanilla until smooth and pourable. Drizzle over cooled cake. Immediately sprinkle colored sugars in sections for the traditional Mardi Gras look.