In a small bowl, dissolve the yeast in the warm water and let it sit until it's frothy, about 5 minutes.

In a large mixing bowl, combine the yeast mixture, sugar, melted butter, warm milk, eggs, and salt. Mix well.

Add the flour and cinnamon, mixing until the dough comes together.

Knead the dough on a floured surface for about 5 minutes, until it's smooth and elastic.

Place the dough in a greased bowl and cover with plastic wrap. Let it rise in a warm place for about an hour, or until it's doubled in size.

In a small bowl, mix together the brown sugar, melted butter, and cinnamon for the filling.

Punch down the dough and roll it out into a long rectangle.

Roll the dough up tightly, pinching the seams together to seal.

Form the dough into a ring and place it on a greased baking sheet.

Cover the ring with plastic wrap and let it rise again for about 30 minutes.

Preheat your oven to 375°F.

Bake the cake for 25-30 minutes, until it's golden brown.

Let the cake cool completely.

In a small bowl, whisk together the powdered sugar, milk, and vanilla extract for the icing.

Divide the icing into three bowls and add a few drops of green, purple, and yellow food coloring to each, creating the traditional Mardi Gras colors.

Drizzle the icing over the cooled cake, alternating colors.

Enjoy your delicious King Cake!