Mardi Gras King Cake

1. 1
   Place the milk and the pinch of sugar in the bowl of a stand mixer fitted with a dough hook and sprinkle the yeast on top. Set aside to rest until the mixture bubbles, about 5 to 10 minutes. (If the mixture doesn’t bubble, either the milk was not at the correct temperature or the yeast was old.) Coat a large bowl with vegetable oil and set aside.
2. 2
   Add the sugar, salt, and zest to the milk mixture and mix on low speed to combine. Add the egg yolks and mix until evenly incorporated. Add the bourbon, orange juice, and almond extract and continue mixing. Add the flour and nutmeg little by little until the dough is moistened throughout and starts to come together. Knead on medium speed until the dough pulls away from the sides of the bowl, forms a ball, and is smooth and elastic, about 5 minutes.
3. 3
   Add the butter piece by piece, letting each fully incorporate before adding the next. Place the dough in the oiled bowl, turn to coat with oil, cover with a damp cloth, and let sit in a warm area until doubled in size, about 1 hour.
4. 4
   When the dough has doubled in size, punch it down, cover, and let rise until doubled in size again, about 1 hour. (Alternatively, you can place it in the refrigerator overnight to rise, about 12 to 16 hours. Be sure to let it sit at room temperature for 10 to 15 minutes before rolling.)

For the filling:

1. 1
   Place the nuts in the bowl of a food processor fitted with a blade attachment and pulse until coarsely chopped, about 5 pulses. Add the remaining ingredients and pulse until you have a coarse meal, about 5 more pulses.

To assemble:

1. 1
   Line a baking sheet with parchment paper and set aside. Roll the dough into a 28-by-8-inch rectangle. Leaving a 1-inch perimeter at the top and bottom (the short sides), spread the filling out along the whole length of the dough.
2. 2
   Whisk together the egg yolk and milk until evenly combined. Brush the exposed perimeter of the dough with the egg wash, fold the long sides of the dough over the filling to form a long cylinder, and pinch the edge to seal. Place the cake seam side down on the baking sheet, form into a ring, and pinch the ends of the dough together to form a circle with about a 3-inch hole in the middle. As needed, press on the circle so that the filling is evenly distributed within the dough.
3. 3
   Cover the cake loosely with a damp towel and set aside to rise until doubled in volume, about 60 minutes. Meanwhile, heat the oven to 350°F and arrange a rack in the middle.
4. 4
   Just before baking, brush the remaining egg wash on the surface of the cake. Place in the oven and bake until the cake has puffed up, the crust is golden, and the underside is golden brown, about 30 minutes. Remove to a wire rack and let cool at least 1 hour.
5. 5
   Hide the baby, if using, in the cake by pushing it up through the bottom of the cake, being careful not to push through the top of the cake.

For the decoration:

1. 1
   Stir together the powdered sugar, bourbon, and orange juice until evenly combined. Brush the cake with the icing and immediately decorate with the green, gold, and purple sugar.