adapted from Lottie + Doof

Cake:

1 package dry yeast (1 1/4 oz)

1/4 cup warm milk

1 cup plus 6 tablespoons bread flour, plus more for rolling

1 tablespoon honey

3/4 cup cake flour

2 eggs

1 egg yolk

4 tablespoons sugar

2 teaspoons ground cinnamon

1 teaspoon vanilla

1/4 teaspoon almond extract

1 teaspoon salt

5 tablespoons butter, at room temperature

Egg Wash:

1 egg

1 tablespoon milk

Frosting:

2 cups powdered sugar

2 tablespoons corn syrup

3 tablespoons milk

1/4 teaspoon vanilla

Green, yellow, and purple sugar for decorating

Whisk the warm milk with the yeast in the bottom of a large mixing bowl, stirring until dissolved.  Add the 6 tablespoons of bread flour and 1 tablespoon of honey.  Using the paddle attachment, mix on low speed until there are no lumps - about 30 seconds - scraping the bottom and sides as necessary.  Cover with plastic wrap and set in a warm place to rise until the dough is doubled in size - about 20 minutes.  

Once the dough is doubled in size, add the remaining 3/4 cup bread flour, cake flour, eggs, egg yolk, sugar, cinnamon, vanilla and almond extracts, and salt.  Mix on low speed until combined and then switch to the dough hook.  Increase the speed to medium and mix until smooth, about 2 minutes.  Increase the speed to medium high and begin adding 4 tablespoons of butter to the dough, 1 tablespoon at a time.  Make sure each tablespoon is well combined before adding the next.  Continue to mix until the dough has formed a slack ball - never heard that one before.  Slack means the dough will ride on the hook without sticking to the sides of the bowl.  

Grease a large bowl with 1/2 tablespoon of the remaining butter.  Transfer the dough to the bowl, cover with plastic wrap and a damp kitchen towel.  Set the bowl in a warm place to rise for at least an hour.  

Line a rimmed baking sheet with parchment paper.  Grease the parchment paper with the remaining butter.  Flour the work surface with 1/4 cup of the remaining bread flour.  Turn the dough out onto the kitchen counter and sprinkle it with more flour.  Roll the dough into a large rectangle (about 24 inches long and 6 inches wide).  Starting with one of the long sides, roll the dough on top of itself, making a long, thin baguette.  Pinch the edges of the dough to seal.  Gently roll the dough on the work surface to even out the roll of dough, making sure it is uniform in size.  Bring the two ends of the dough together and pinch it together to form a seal.

Carefully transfer the circle of dough to the baking sheet.  Cover the dough with a piece of plastic wrap and a damp kitchen towel.  Let it rise until the dough has doubled in size, about an hour.  

Heat the oven to 375.  To make the egg wash, whisk the one egg with the milk until a smooth mixture has formed.  Brush the egg wash over the sides and top of the dough.  Bake the king cake until golden brown and cooked through - about 25 minutes.  Let the cake cool completely.  

To make the frosting, whisk together the powdered sugar, corn syrup, milk, and vanilla in a bowl.  Spoon the icing over the cooled cake.  Top sections of the cake with alternating colors of sugar.  Serve immediately.