01 - Combine warm water, a pinch of sugar, and yeast in a small bowl. Let stand until foamy, approximately 5 minutes.
02 - Whisk together milk, eggs, softened butter, sugar, salt, nutmeg, and vanilla extract in a mixing bowl. Add the foamy yeast mixture and combine thoroughly.
03 - Gradually incorporate flour until a soft dough forms. Knead by hand or with a dough hook for 8 to 10 minutes until smooth and elastic.
04 - Place dough in a greased bowl, cover, and let rise in a warm area until doubled in size, approximately 1 to 1.5 hours.
05 - Punch down dough and turn onto a lightly floured surface. Roll into a 10x20 inch rectangle.
06 - Mix brown sugar and cinnamon. Brush the dough rectangle with melted butter, then evenly sprinkle the cinnamon-sugar mixture across the surface.
07 - Roll tightly from the long side to create a log. Pinch the seam firmly to seal.
08 - Transfer to a parchment-lined baking sheet and form into a ring, pinching ends together securely. If following tradition, insert a plastic baby or bean from underneath.
09 - Cover and let rise until puffy, approximately 45 minutes. Preheat oven to 350°F.
10 - Bake for 25 to 30 minutes until golden brown. Cool completely on a wire rack.
11 - Stir powdered sugar, milk, and vanilla extract until smooth and pourable consistency is achieved.
12 - Drizzle icing over cooled cake. Immediately sprinkle colored sugars in sections to create traditional Mardi Gras presentation.