My recipe is modified from this one from All Recipes.
4 teaspoons active dry yeast
1/2 C white sugar
1 C warm milk
1/2 C butter, melted and mostly cooled
5 egg yolks
4 1/2 C all purpose flour + more for kneading
2 teaspoons salt
1 teaspoon ground nutmeg
1 teaspoon grated lemon zest
for the filling:
1 8oz package cream cheese, softened
1/2 C powdered sugar
for the icing:
2 C powdered sugar
scant 1/4 C lemon juice
1 tablespoon milk
green, yellow, and purple sprinkles
Melt the butter and set aside so it can cool a bit. Preheat the oven to 175; when it reaches the temp turn off the oven so it is the right temperature for raising the dough.
Mix the first three ingredients together; set aside for about 10 minutes while yeast activates.
Blend butter and egg yolks in a large bowl.
In a separate bowl mix together flour, salt, nutmeg, and lemon zest.
Combine yest and butter mixtures. When well blended, add the flour mixture. When the dough has gathered into a ball in the bowl, dump it onto a lightly floured surface to knead. Add flour as needed; the dough should be soft but not sticky.
Take a large, oven-proof bowl (I use a large, glass bowl - the same one I mix in so I have to quickly wash it out.) and lightly coat with canola oil. Put the dough in the bowl and flip it over so the top of the dough is coated with oil. Loosely cover with a damp towel (I used a wet paper towel) and place in a warm oven. It should take 1-2 hours for the dough to double. Meanwhile mix the cream cheese and powdered sugar.
When doubled, remove the dough from the bowl and roll out into a long, thin rectangle, approximately 6"x30". (You could also divide the dough in half and make two smaller King Cakes.) Spread the cream cheese filling down the center of the rectangle. Fold the two sides over the filling, creating a thick rope. Pinch the ends of the rope shut so the filling won't bake out.
Place the rope on a lightly greased baking sheet, seam side down. If you have a baby Jesus to bake into it, put it in now. Position the dough so the hole in the center is large and won't fill in as the dough rises again. Put a damp cloth on it again and place in a re-warmed oven so it can rise again. This will take 30-60 minutes.
When the dough has raised again take out of the oven and preheat it to 350 degrees. Bake for 25 minutes. Meanwhile, mix the ingredients for the icing.
When the King Cake has cooled frost with the lemon-icing. Add purple, green, and yellow sprinkles.