1. In a small bowl, dissolve the yeast in the warm water and let sit for 5 minutes until foamy.

2. In a saucepan, heat the milk over medium heat until just simmering. Remove from heat and stir in the sugar, butter, and salt until the butter is melted. Allow to cool to lukewarm.

3. In a large bowl, combine the yeast mixture, milk mixture, and 3 cups of the flour. Knead the dough until it forms a smooth, elastic ball, adding more flour as needed.

4. Place the dough in a greased bowl, cover, and let rise in a warm place for 1 hour or until doubled in size.

5. In a skillet, sauté the crawfish and corn over medium-high heat for 5-7 minutes until the crawfish are cooked through and the corn is tender. Remove from heat and let cool slightly.

6. In a food processor, blend the cream cheese, green onions, and Cajun seasoning until smooth.

7. Punch down the dough and roll it out into a large rectangle, about 1/4 inch thick. Spread the cream cheese mixture over the dough, then top with the crawfish and corn mixture.

8. Roll the dough into a tight log, then shape it into a ring and place it on a greased baking sheet. Pinch the ends together to seal.

9. Cover and let rise for 30 minutes.

10. Preheat the oven to 350°F.

11. Brush the top of the king cake with the beaten egg.

12. Bake for 25-30 minutes, until golden brown. Allow to cool slightly before slicing and serving.