King cake recipe New Orleans style

The day before, begin making the dough.
In a small bowl, mix warm milk and sugar. Sprinkle yeast over the top. Let it sit for about 5 minutes until it gets all bubbly.
In the bowl of a stand mixer, combine flour, salt, eggs, and vanilla extract. Pour in the yeast mixture. Use the dough hook attachment and mix for 1 minute at low speed, and 5 minutes at medium speed until it forms a smooth dough.
Slowly add the chunks of room-temperature butter to the dough, allowing each piece to incorporate before adding more.
Place the dough in a large bowl, cover it with plastic wrap, and let it rest in the refrigerator overnight.

To make the filling, place butter, brown sugar, and cinnamon in a medium bowl and use a hand mixer, or stand mixer with a paddle attachment to combine the mixture until it is smooth. Store at room temperature, in an airtight container until ready to use.

The next day: shape the King Cake.
On a floured surface, roll the dough into a large rectangle about 12 x 18 inches.
Spread the filling on the rectangle of dough evenly. Place the small plastic baby in the filling and roll the dough up to make a log. Pinch the two ends together to make a circle. (The longer your rectangle, the bigger the circumference of your cake will be)
Place the ring onto a baking sheet that has been lined with parchment and brush with egg wash. (To make egg wash, mix 1 egg yolk with 1 Tbsp. water and mix until smooth. Use a pastry brush to apply the egg wash to the dough)
Cover the dough with a clean kitchen towel and allow the King Cake to rise in a relatively warm envirornment for 60-90 minutes or until doubled in size.
After the dough has risen, preheat the oven to 350 degrees F. Bake for 30-35 minutes, or until golden brown. If you notice the top is getting too brown, loosly drape with aluminum foil.
Remove the pan from the oven and place it on a wire rack to cool while you make the icing.

In a small bowl, using a whisk, mix the powdered sugar, water, and meringue powder until smooth and lump-free.
Transfer the King Cake to a wire cooling rack with a baking sheet under it to catch the drips of icing. Glaze the cake by pouring the icing over the cake, making a zig-zag motion from the center of the cake to the outside edges, working your way all around the cake.

Add the Colored Sugar to the top of the cake in a striping motion alternating green, purple, and gold stripes. Top with a few strands of Mardi Gras beads and a few gld coins.
Serve immediately or store for up to 5 days at room temperature.