Step 1

Make the dough. In the bowl of a stand mixer fitted with the dough hook, combine the all-purpose flour, sugar, yeast, and salt. Knead on low to combine, about 30 seconds. With the mixer on low, add the eggs and egg yolk, one at a time, only adding the next egg when the previous one is fully incorporated. Use a tall glass to press down into the center of the mixture to make a well in the center of the ingredients.

Step 2

Knead the dough, In a liquid measuring cup, whisk together the melted butter and water. Pour the mixture into the well and knead on medium-low for 10 minutes, or until sticky and elastic, using a rubber spatula to scrape down the bottom and sides of the bowl as necessary.

Step 3

Prep the dough for rising overnight. Tip the dough out onto a lightly floured counter. Dust your hands with flour and knead the dough once or twice into a rough ball. Scrape down the bottom and sides of the bowl to remove any excess dough. Spray the bowl with cooking spray and place the dough back in the bowl. Cover with plastic wrap. Refrigerate overnight.

Step 4

First, make the cream cheese filling. In the bowl of a stand mixer fitted with the paddle attachment, beat the cream cheese on medium-low until soft, about 1 minute. Add the brown sugar and beat until light and fluffy, about 1 minute, using a rubber spatula to scrape down the bottom and sides of the bowl as necessary. Reduce the mixer to low and add the egg yolk, cinnamon, and salt, beating until combined. Scrape down the bottom and sides of the bowl once more, and beat on medium-high for an additional 30 seconds.

Step 5

Next, shape the cake. Uncover the dough and discard the plastic wrap. Tip it onto a lightly floured counter. Use a rolling pin to roll the dough into a large rectangle about 12 inches wide and 20 inches long. Press a bench scraper against the sides of the dough to create straight edges. Use an offset spatula to spread the cream cheese filling evenly across to the edges, leaving a 1-inch gap between the filling and the short ends. Starting from one of the long ends, roll the dough into a tight, even log. Bring the ends of the log together to form an oval ring, moistening and pinching the edges together to seal.

Step 6

Prep the dough for rising again. Place on a parchment-lined sheet pan. Cover with plastic wrap and let sit in a warm spot for 1 to 2 hours, or until puffy and your finger leaves an indent when gently poking the dough.

Step 7

Prep the oven. About 30 minutes into this rise, position a rack in the center of the oven and preheat to 375°F.

Step 8

Bake the cake. Bake the king cake for 35 to 40 minutes, or until the outside of the cake is golden brown and an instant read thermometer inserted into the center of the cake reads 200°F. Cool on a wire rack completely.

Step 9

Dye the sanding sugar. As the cake cools, make the sugar topping. Divide the sanding sugar evenly between three zip-top bags. Add one generous drop of green food coloring in one bag, one generous drop of purple food coloring in the second bag, and one generous drop of yellow food coloring in the third bag. Seal the bags. Shake each bag until the food coloring is distributed evenly into the sugar. Pour each of the dyed sugars onto its own separate plate and use a rubber spatula to spread them evenly across the plate to dry.

Step 10

Make the icing. Once the cake is cool, make the icing. In a medium bowl, combine the confectioners' sugar, milk, and lemon extract. Use a rubber spatula to mix until combined; the paste will be thick. Immediately pour the icing into a piping bag fitted with a small tip.

Step 11

Decorate the cake. Pipe long, thin lines of icing directly onto the king cake, covering it completely. Immediately sprinkle with the dyed sanding sugars.

Step 12

Serve and store. Serve immediately, or wait 1 to 2 hours for the icing to harden before serving. The king cake can be stored at room temperature for up to 3 days.