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Make the dough: In the bowl of a standing mixer combine yeast, warm water, and 1 teaspoon of the sugar. Stir to combine and let sit until foamy and tripled in volume, about 10 minutes. Add remaining sugar, milk, light brown sugar, vanilla, egg, and egg yolks and whisk to combine. Add flour and salt and mix on medium-low speed with a dough hook and knead dough for 5-8 minutes, until the dough pulls away from the sides of the bowl and forms into a ball on the hook. Reduce the speed to low and add the butter a couple of tablespoons at a time, waiting until most of the butter is absorbed before adding more. Continue to knead about 2-5 minutes, until the dough passes the windowpane test (see note below).
Transfer the dough to a greased bowl, cover with plastic wrap, and let sit in a warm, draft-free place until doubled in size, about 1 ½ –2 hours. Alternatively, place the covered bowl in the refrigerator overnight for a slow proof.
While the dough rises, make the fillings: Combine cream cheese, powdered sugar, vanilla and salt in a medium bowl with a hand mixer until well-combined and fluffy. Transfer the mixture to a piping bag and set aside. In a small bowl, combine the cinnamon and sugar; set aside. In another small bowl, use a fork to whisk together the egg and water for the egg wash. Set aside.
Line two baking sheets with parchment paper. Use aluminum foil to create 4 balls about 1-inch large and coat with baking spray; set aside. Once the dough has risen, lightly punch down dough and turn it out onto a very lightly floured work surface. Use a knife to divide the dough in half. Using a rolling pin, roll the first half of dough into a 20x6-inch rectangle. Use just enough flour to make rolling out possible, you don’t want to over-flour.
Use a pastry brush to lightly coat the surface of the dough with melted butter, leaving about 1-inch unbrushed along the top edge. Lightly sprinkle the entire surface with half of the cinnamon sugar mixture, trying to avoid the top inch.
Cut about 1-inch off of the tip of the piping bag and pipe a line of cream cheese filling along the long bottom edge of the dough.
Use your fingertips to lift the bottom of the dough up and over the cream cheese, and gently continue to roll the dough all the way up until it meets the other end. Use your fingers to pinch the seam together, then trim the uneven ends off and discard (no more than 1-inch per side). Use a knife to cut the roll into two even halves. Gently push the two ends of one half together to form a circle and pinch the dough together on all sides, being careful not to let any of the cream cheese squeeze through.
Repeat with the second half and set both circles on one prepared baking sheet. Repeat this entire process with the other half of dough. Place one foil ball in the center of each dough circle to help keep the shape while baking. Cover with plastic wrap and let sit for about 30 minutes. Preheat the oven to 350°F (175˚C).
Uncover cakes and brush all over with egg wash. Place in the oven and bake until golden brown, about 20-25 minutes, until an instant-read thermometer inserted into the dough reaches 190˚F (87˚C) and the cakes are golden brown. Let cool for 10 minutes before transferring to a wire rack to cool.
While the cakes bake, make the glaze: in a medium bowl, whisk together the powdered sugar and milk until smooth. It should be the consistency of royal icing, thick but still flowing. Set the rack over a baking sheet. Once the cakes are mostly cooled, pour icing evenly over the cakes so that it drips slightly over the sides. Decorate immediately with sprinkles in an alternating pattern before the icing dries, or frost then sprinkle individually.
While the cakes cool, make the maple glaze: In a small saucepan over medium heat, add the butter, brown sugar and maple syrup. Once the butter has melted and the sugars have started to dissolve, add the pecans and salt. Let the sauce bubble and thicken for 2 minutes, then remove from heat and carefully add the heavy cream. Return to heat and let boil for another 3-4 minutes. Remove from heat and let cool for a moment.
To serve, stack the mini king cakes on top of each other and carefully spoon the maple pecan glaze all over the stack.
Note: Using wet fingers, gently use your hands to stretch a small portion of the dough apart. If the dough tears quickly, the gluten is not developed enough yet and you need to knead for longer. If the dough stretches thinly without breaking and you can see light through it, the dough is ready.
Tips: -Measure flour properly by spooning flour into a measuring cup then leveling off the excess with a flat-edged knife, rather than scooping up the flour directly from the container. -Use the inside of the leftover butter wrapper to grease the bowl the dough will rise in.