First, gather all of the filling ingredients, including butter, brown sugar, and cinnamon. In a medium bowl, combine these ingredients with a fork until they’re thoroughly mixed. Set this filling aside; the aroma will tantalize your senses!
In a small bowl, warm the milk to between 110 to 120°F. Whisk in the sugar and yeast until everything is blended well. Let the mixture sit for about 7 to 10 minutes until it becomes foamy. This is crucial; if it doesn’t foam, your yeast may not be active.
Next, in the bowl of a stand mixer, add the melted butter, one whole egg, egg yolks, vanilla, and the foamy yeast mixture. Use the paddle attachment to mix everything together for about 30 seconds until combined.
With the mixer still running on medium speed, gradually add the flour until the mixture is completely combined. The dough should start to form. It’s time to change out the paddle attachment for the dough hook.
Knead the dough on medium speed for 7 minutes. You’re looking for a texture that pulls away from the bowl and becomes smooth and elastic. If it’s too sticky, you might need to add a touch more flour.
Remove the dough from the bowl and shape it into a smooth ball using your hands. Lightly spray a large bowl with cooking spray or oil, and then place the dough inside. Cover it with plastic wrap and set it in a warm, draft-free area to rise until it doubles in size, usually about 1 to 2 hours.
Once the dough has risen, preheat your oven to 375°F. Gently punch down the dough to release any air pockets before transferring it to a lightly floured surface.
Divide the dough into two equal parts, using a knife or bench scraper. Roll each portion into a rectangle approximately 24 inches long and 5 to 6 inches wide.
Spread the prepared cinnamon filling evenly over each rectangle, leaving a one-inch border around the edges. Roll each rectangle tightly from one end to the other, pinching the seams to seal them well.
Braid the two rolled pieces together, forming a circle and sealing the ends. Place the unbaked cake onto a large baking sheet lined with parchment paper.
In a small bowl, whisk together one egg and a tablespoon of water. Brush this egg wash over the top of your dough braid. Bake for 25 to 30 minutes, covering it with foil after about 15 minutes to prevent over-browning.
Once baked, remove the cake and allow it to cool completely on a wire rack.
Prepare the icing by mixing the powdered sugar, melted butter, vanilla, and milk in a bowl using an electric hand mixer until it’s smooth and spreadable. It should hold its shape and not be too runny.
After the cake has cooled, press the hidden baby into one of the folds of the braided cake. Use a spatula to cover the top with the icing generously, and then sprinkle the glitter sugar over the icing in alternating colors of purple, green, and gold.
Serve your Mardi Gras King Cake immediately, or cover it with plastic wrap until you're ready to share. Enjoy!