Prepare the dough: In a large bowl, combine warm milk and sugar. Sprinkle yeast over the milk and let it sit for 5–10 minutes until bubbly.
Mix dough: Add flour, salt, cinnamon, softened butter, eggs, and vanilla to the yeast mixture. Use a stand mixer or hand mixer to combine, then knead for about 5-7 minutes until the dough is smooth and elastic.
Let the dough rise: Place the dough in a lightly oiled bowl, cover with a clean kitchen towel, and let it rise in a warm place for 1 to 1.5 hours, or until it doubles in size.
Prepare the filling: In a small bowl, mix the brown sugar and cinnamon together. Set aside.
Roll out the dough: Once the dough has risen, punch it down and roll it out into a large rectangle (about 12x18 inches) on a floured surface.
Add the filling: Brush the dough with melted butter, then sprinkle the cinnamon-sugar mixture evenly over the dough.
Form the cake: Starting from one of the longer sides, tightly roll the dough into a log. Pinch the ends to seal. Form the dough into a circle and pinch the ends together to create a ring shape.
Bake the cake: Preheat oven to 350°F (175°C). Place the King Cake on a baking sheet lined with parchment paper. Let it rest for 20 minutes while the oven heats. Bake for 25–30 minutes, or until golden brown.
Prepare the glaze: In a bowl, whisk together powdered sugar, milk, and vanilla extract until smooth.
Glaze and decorate: Once the King Cake has cooled slightly, drizzle the glaze over the top. While the glaze is still wet, sprinkle on the purple, green, and yellow sugars in sections, creating vibrant stripes of color. If using, hide the baby figurine or dried bean inside the cake (traditionally placed under the glaze).
Serve: Let the cake cool completely before slicing and serving. Enjoy!