In a glass bowl, mix the milk and water, microwave at 20-second intervals until the milk is warm (around 115°F or 45°C).

In a large mixing bowl, add in the warm milk, yeast, and a teaspoon of granulated sugar, and mix until combined. Allow to sit for up to 10 minutes until the yeast is foamy (if it isn't, start all over).

Add in 2 cups of flour, the remaining granulated sugar, melted butter, cinnamon, nutmeg, egg, egg yolks, and salt. Mix until just combined.

Gradually add in the remaining flour while mixing until the dough is well combined and sticking to itself as you mix (it should be a bit tacky when you touch it).

Transfer the dough to a flat, floured surface, and knead for about 10 minutes until you have a smooth and elastic dough.

Get a large bowl and lightly oil it, now, place the dough in the bowl and cover with a plastic wrap. Allow to sit for 1-2 hours in a warm, dry place until it has risen to double its size.

In a bowl, whisk together brown sugar, cinnamon, and salt.

Now, deflate the risen dough, and transfer to a flat, floured surface. Roll into a rectangular shape about 10x20-inch. Now, cut it into two lengthwise.

Now, spread the softened butter evenly over each rectangle, leaving a 1-inch allowance around all sides.

Sprinkle the filling mix evenly over the butter, then roll each rectangle lengthwise into a rope-like shape, and pinch the edges to properly seal it.

Now, take each rope-like dough and twist it to form a wreath. Transfer it to a baking sheet lined with parchment paper.

Cover with a towel, and allow to sit for about 45 minutes until it has risen to double its size.

While waiting for the dough to rise in size, preheat your oven to 350°F (or 175°C). Prepare an egg wash by whisking 1 egg and a tiny bit of water.

Once the dough is risen, brush over the surfaces with the egg wash. Transfer to the preheated oven, and bake for 30-35 minutes, or until the bread is golden brown. Take out of the oven and allow to cool completely.

In a bowl, whisk together milk, vanilla extract, and powdered sugar. Make sure it has a thick but runny texture.

Drizzle the glaze over the cooled king cake, and then decorate with some purple, gold, and green sanding sugar.