By no means is this a "traditional king cake recipe". Truth be told, what many think of as a "traditional king cake" is not traditional either. La Galette des Rois is the original king cake, made for centuries in France. Many from South Louisiana come from French heritage, hence the tradition of king cakes but with different iterations along the way. This is my interpretation.
Heat milk to 100°-110°. Stir yeast into warm milk & let stand for 10 minutes. If bubbles form, you have active yeast & you are good to go.
If not, your yeast is dead & you need to go out to buy more.
Whisk flour and water together in microwaveable dish or measuring cup until smooth. Microwave, whisking every 25 seconds until stiff and pudding-like, 50-75 seconds. Should mound instead of spread when dropped from a spoon. Let cool to ~115° in metal mixing bowl.
In bowl of stand mixer, whisk flour paste and milk/yeast together until smooth. Whisk in egg and yolk until uniform. Add flour.
Fit stand mixer with paddle attachment and mix on low until uniformly moist, ~1-2 minutes. Stop and let stand 15 minutes.
Replace paddle with dough hook. Add sugar and salt and mix on medium-low for 5 minutes.
Stop and add softened butter cut up into slices. Mix on medium-low for 2.5 minutes. Scrape down hook and bowl. Mix 2.5 minutes more on medium-low.
Dough should form a nice ball in the mixing bowl. If not, transfer to a floured counter and knead to form a tight ball. Place in a lightly greased bowl, lightly coat dough with vegetable spray and cover with plastic wrap.
You can either continue on or place your dough in the refrigerator overnight to cold ferment.
Let dough rise until doubled in volume, 40 minutes - 1 hour
Melt butter over medium heat in a small saucepan. Butter will foam and pop, then start to brown as the solids toast. You can go as light or dark with your browning. It will smell nutty and wonderful.
Make right before brushing on dough or make while dough rises & remelt.
On a flour dusted work surface, flatten dough & shape into a 12" square. Let rest 10 minutes.
Roll to 1/4" thin forming a rectangle.
Let rest 10 minutes.
Roll to 1/8" thin.
Let rest 10 minutes.
Roll to 1/16" or thinner.
It will be at least 4.5 feet long.
Brush on melted brown butter over the entire dough.
Using a pizza cutter, slice dough in half lengthwise. Place one half on top of the other. Repeat. You should now have 4 layers of 4 ft dough.
Cut in half through the middle making two 2 ft pieces. Roll out both pieces to around 4 ft again. If dough wants to spring back, let it rest for 10 minutes and try again.
Brush tops with melted brown butter. Make more if you need to. More butter is always welcome. Sprinkle with brown sugar. You want a very thin layer over the entire dough. Pat into place.
Roll each 4 ft piece tightly into a cylinder. Place seam side down on a parchment lined sheet pan and refrigerate for 15 minutes.
Mark every inch with a very sharp knife to use as your guide. To slice, hold a strand of dental floss taut and slide underneath the cylinder, stopping at the first mark. Cross ends of floss over each other and pull.
Transfer each slice, cut side down, to your parchment lined baking sheet, cover with plastic wrap and let chill in fridge for 45-55 minutes.
Preheat oven to 375°F
Place slices on new parchment paper in a circle for traditional king cake shape or space out to make individual cakes.
Bake 25-30 minutes, turning halfway through for even color until golden brown.
Top with Brown Butter Cream Cheese Icing while warm.