Heat up the milk in the microwave or stovetop to 100 to 110 F/37 to 43 C. Then sprinkle on the yeast and a pinch of sugar. Let it stand for 5 to 10 minutes until it gets foamy.
Now add the sugar, melted butter, sour cream, and eggs. Whisk to combine. The sour cream is optional but I always add it.
In a separate bowl combine the salt and the flour. Then add the flour 1/3 of it at a time, stirring it in with a spoon, or use a stand mixer. Once the dough has come together and is slightly tacky it is ready to be kneaded.
Knead the dough for 8 minutes on a floured surface or use a stand mixer with a dough hook. Adding a bit of flour as needed to keep it from sticking.
Place the dough into a large bowl with a little bit of oil in it. Roll the dough ball around so it gets coated with the oil. This will help it to not dry out while it rises. Cover the bowl with plastic wrap or a damp cloth and place it somewhere warm and let it rise for 60 to 90 minutes, until doubled in size.
Punch down the dough and place it on a floured surface. Use a rolling pin and roll it into roughly a 10 inch by 18-inch rectangle.
In a small bowl combine the softened butter and brown sugar and cinnamon. Spread it onto the rolled out dough.Alternatively, you can baste the dough first with the butter and then sprinkle on the cinnamon and sugar mixture.
Now, start at one end and roll up the dough fairly tightly lengthwise. Then place it onto a sheet pan lined with parchment paper or a silicone mat. Curl it in creating a circle and crimp together the to ends. Cover with plastic wrap and allow it to rise for another hour. Remove the plastic wrap and it is ready to go. Preheat the oven to 375 F/190 C.
Bake the cake/giant cinnamon roll for 25 to 30 minutes until nice and brown on top. Remove it from the oven and allow it to cool for 15 minutes. Tradition calls for a little plastic baby to be put in the cake. Originally symbolizing baby Jesus.
Now cut a slit into the middle of the cake, and stuff the little baby inside. Or you can turn the cake over and cut the slit in the bottom somewhere and stuff it in there.
In a small bowl mix together the powdered sugar, vanilla extract, and the milk. Add more milk or powdered sugar as necessary to get your desired thickness. Cover the top of the cake with the glaze. Then sprinkle on the colored sanding sugar, alternating between the colors. The classic colors are yellow, green, and purple.
The Mardi Gras king cake is done and ready to serve. Enjoy!