Combine the warm water, about 1 tablespoon of the sugar, and the yeast.
Stir, then let it sit for 5-10 minutes until the yeast is foamy.
Once the yeast is foamy, add the milk and butter, the remaining sugar, eggs, vanilla, and 1 cup of the flour.
Mix well, then continue adding flour while kneading with the dough hook attachment, 1 cup at a time.
Knead for 5 minutes on medium speed or 8-10 minutes by hand to create a very soft dough that starts coming away from the sides of the bowl.
Turn out the dough onto a floured surface and knead a few times by hand until a smooth, round ball forms. Clean and lightly oil the bowl, then return the dough to the bowl, turning to coat.
Cover with plastic wrap and let rise in a warm place for 1-2 hours until doubled in size.
For the cinnamon filling, combine the brown sugar, granulated sugar, flour, cinnamon and butter, mixing to combine. Set aside.
Once the dough has doubled in size, punch it down and divide in half.
Roll out one half of the dough into a large rectangle on a lightly floured surface, roughly 10x16-inches. Use a pizza cutter to divide the dough in half lengthwise to create two long rectangles.
Crumble the cinnamon filling evenly over the dough.
Roll up into two long cylinders, just like when making cinnamon rolls.
Twist the two logs together into a rope braid, then transfer to the prepared baking sheet.
Shape into an oval and pinch the ends together. Repeat with the remaining dough and filling. Cover lightly with plastic wrap and let rise for 30-45 minutes until puffy.
Bake for 25-30 minutes until golden brown and baked through. Remove from oven and cool completely before frosting.
Stick a plastic baby figurine into each cake, pushing it down in to hide it.
Beat the powdered sugar, milk, butter, lemon juice, and vanilla in a medium bowl until smooth. Drizzle the frosting over both king cakes, spreading it with a spatula if needed for good coverage.
Sprinkle with the purple, green, and gold sugar while the frosting is still wet before it has a chance to set.
If you have never had King Cake before, you can think of it as a cross between a Danish pastry and a giant cinnamon roll shaped like a wreath and covered with colored sugar sprinkles.
One fun and quirky thing about king cake is the tradition of the tiny baby figurine hidden inside, which symbolizes prosperity and luck. Whoever ends up with the slice with the baby is said to be King or Queen for the day!