Mardi Gras King Cake

Lightly grease a baking sheet, or line it with parchment., To prepare the dough: Using a stand mixer, electric hand mixer, or bread machine, mix and knead all of the dough ingredients together to form a smooth, very silky dough. You may try kneading this dough with your hands, if desired; but be advised it's very sticky and soft., Allow the dough to rise, covered, for 1 hour. It'll become puffy, though it probably won't double in size., Transfer the soft dough to a lightly greased work surface. Pat and stretch it into a 24" x 6" rectangle. This won't be hard at all; it's very stretchy. Let the dough rest while you prepare the filling., To prepare the filling: Beat together the cream cheese, sugar, and flour until smooth, scraping the bowl once. Add the egg and flavor, again beating until smooth., Dollop the filling down the center of the long strip of dough. Then fold each edge up and over the filling until they meet at the top; roll and pinch the edges together, to seal the filling inside as much as possible., Place the log of dough onto the baking sheet seam-side down. The dough will be very extensible, i.e., it'll stretch as you handle it. So pick it up and position it on the pan quickly and gently. Pinch the ends together., Cover and let rise for about an hour, until it's puffy. Preheat the oven to 350°F while the dough rises., Whisk the reserved egg white with 1 tablespoon water, and brush it over the risen cake., Bake the cake for 20 minutes, then tent it lightly with aluminum foil. Bake it for an additional 30 minutes, until it's a rich golden brown., Remove the cake from the oven. After about 15 minutes, transfer it from the baking sheet to a rack to cool., To make the icing: Beat together all of the icing ingredients, dribbling in the final 2 teaspoons milk until the icing is thick yet pourable., Pour the icing over the completely cooled cake. While it's still sticky, sprinkle with alternating bands of yellow, purple, and green sugars. Space candied cherries in a ring around the top.