Mix 1 1/2 cup of the flour, granulated sugar, salt and yeast together in a mixer bowl.
In a small saucepan over low heat, heat the milk, water and butter to 120-130 degrees F. Add to dry ingredients in the mixing bowl. Beat on medium to fully combine.
Add the eggs and ½ cup flour. Beat until fully combined on medium speed (1-2 minutes).
Add the rest of the flour (1 cup, 3 tablespoons); beat on medium-high to fully combine (1-2 minutes). Dough will be pliable.
Form dough into a ball with hands or mixing spoon in the mixing bowl (or mixer bowl if using a standing mixer). Lightly oil (sunflower oil; mild taste oil) the surface of the dough. Cover with damp, warm lightweight towel and place in warm, draft-free area until the dough doubles in size (approximately 1 hour). Note: if a warm, draft-free spot is not available, preheat oven to 200 degrees, turn off the oven, crack the door to release some heat and place rising dough in oven with door closed.
Punch dough down. If the dough is too sticky to work with, place bowl with dough in the refrigerator for 10 minutes.
Prepare an area to roll out dough. It is recommended to roll dough out on a Roulpat or other rolling mat or wax paper to aid in finally rolling the dough into a jelly roll. Lightly flour the rolling surface.
Using a rolling pin, roll dough into a rectangle approximately 22 inches long by 12 inches wide. !Adding the filling:
Combine the granulated sugar and cinnamon in a bowl. Line a large baking sheet with parchment paper and spray the parchment paper with cooking spray; set aside.
Spread softened cream cheese to cover the top of the dough. Sprinkle the sugar-cinnamon mixture on top of the cream cheese.
Using one side of the rolling mat (on a long end of the dough) gently lift the mat up allowing the edge of the dough to roll over onto the cream cheese filling by about 2 inches. Lift the mat again to roll the dough over on itself again by about 2 inches. The dough can be adjusted to be rolling evenly between each lifting of the mat. Repeat until the dough is rolled up into a 2-3 inch wide roll with the seam at the bottom.
Shape dough into an oval with the ends touching; pinch them together using water-moistened fingers to smooth the seam.
Gently move the oval to the prepared baking sheet. Cover with plastic wrap and place in a warm draft-free area to rise approximately an hour or until the cake has doubled in size.
While the King's Cake is rising, preheat the oven to 350 degrees. When the cake has doubled in size place it in the preheated oven and bake until the cake is lightly golden on top; approximately 30 minutes. Remove from the oven and allow to cool fully on the pan.