This rich king cake is filled with salted caramel and glazed with more caramel, dusted with the signature colors of Mardi gras: purple, gold, and green.
Transfer dough to a greased bowl, cover with a damp towel or saran wrap, and let rise for one to two hours, in a warm place, until doubled in size.
While the dough rises, make the filling. In a large sauce pan on medium heat, melt together the butter and brown sugar and continue stirring until the mixture starts to bubble. Remove it from heat, stir in the heavy cream, and transfer it to a heatproof bowl. Divide in half (one half of the salted caramel will be inside the cake, and the other half you will mix into the glaze). Cool filling in the fridge for at least an hour. (Caramel filling can be made up to five days ahead. Keep in fridge covered).
After dough has doubled, punch it down and divide it in two balls. Shape the first piece into a rectangle. With a rolling pin, roll it out to a roughly 13-inch long rectangle. Spread 1 cup of the filling on evenly, leaving an inch along one of the long sides so that the filling doesn't ooze out. Starting opposite of that end, roll up the dough like a jelly roll. Repeat for the other ball of dough. Pinch seams and ends closed thoroughly (wet your fingertips if it's easier). Braid the two logs together.
Transfer to a greased baking sheet and shape the cake into an oval, joining the ends and pinching them together. Let rise for another half an hour.
To make the glaze, beat the cream cheese with the milk until smooth. Beat in 1/4 cup of caramel. Alternate adding powdered sugar and milk until glaze is thick but still pourable. Place the cake on a wire rack over parchment and pour glaze over cake. Decorate with sanding sugar, alternating purple, green, and gold. Working from the bottom of the cake, press the baby fully into the cake.