Combine milk and water and heat in 20-second increments in a microwave-safe container (I use a glass measuring cup) until the temperature reads between 105-115F (40-46C) with an instant read thermometer (always stir before checking the temperature).
Pour liquid into a large mixing bowl (or this recipe may be made in the bowl of a stand mixer with the dough hook attachment), add yeast and a teaspoon of the granulated sugar and stir until combined. Allow to sit until yeast is foamy (5-10 minutes). Note that if your yeast does not foam you will need to start over.
Add remaining granulated sugar, melted butter, egg, egg yolks, salt, cinnamon, nutmeg, and just 2 cups (250g) of flour and stir until all ingredients are well-combined.
Gradually stir in additional flour until your dough is well-combined and clinging to itself as you mix. It should be slightly tacky to the touch but not so sticky that it’s sticking to your fingers. You may not need all 5 cups of flour, or you may need more.
Turn dough out to a clean, lightly floured surface and knead for 5-10 minutes or until you have achieved a smooth, elastic dough. Add additional flour as needed if dough is sticking to your hands (with a stand mixer you will just mix with dough hook on low speed until proper consistency is reached).
Place dough in a clean, lightly oiled large bowl and cover tightly with plastic wrap. Allow to rise in a warm, draft-free space until doubled in size (about 1-2 hours).
Whisk together brown sugar, cinnamon, and salt until combined. Butter should be soft enough to be spreadable, pop it in the microwave for several seconds if needed!
Gently deflate dough and turn out onto a clean, lightly floured surface. Roll into a neat 10×20” rectangle and then cut in half lengthwise.
Spread softened butter evenly over the surface of each rectangle, leaving a ½” (1.3cm) perimeter around all sides.
Sprinkle butter evenly with filling. If using a plastic baby you would place it somewhere in the rectangle before rolling.
Roll each rectangle lengthwise tightly into a rope and pinch the edges to make a seam.
Twist the two ropes together to form a wreath and transfer to a parchment paper lined baking sheet.
Cover with a towel and allow to rise until increased in size, about 45 minutes.
While dough is rising, preheat oven to 350F (175C) and prepare an egg wash by whisking together 1 egg and a teaspoon of water.
Once dough has risen, remove towel and lightly brush all over with egg wash. Transfer to preheated oven and bake for 30 minutes or until bread is golden brown and sounds hollow when tapped, or preferably when a thermometer inserted in the thickest part reads 190F (87C). Allow to cool completely before decorating.
Prepare glaze by whisking together powdered sugar, milk, and vanilla extract. Glaze should be thick enough that when it drizzles off your whisk it should hold its shape for several seconds before dissolving back into the rest of the glaze in the bowl (add more milk if it’s too stiff and more sugar if it’s too thin).
Drizzle glaze all over cooled king cake then decorate immediately with colored sprinkles, alternating patches of green, purple, and yellow sugar. Slice, serve, and enjoy!