Combine the milk, water, and yeast in the bowl of a stand mixer fitted with the dough hook attachment. Let stand for 5 minutes or until the yeast is foamy and slightly bubbly. Beat in the butter, egg, egg yolks, and sugars until smooth, about 1 minute.
Add both flours and salt; beat on medium-high speed until dough pulls away from the sides of the bowl and is no longer too tacky, about 5 to 7 minutes.*
Transfer the dough to a lightly greased bowl and cover tightly with plastic wrap. Place the bowl in a warm place (I heat my oven to 95°F and place the bowl in the bottom of the oven) until doubled in size, about 45 minutes to 1 hour.
Turn the dough out onto a lightly floured surface. Roll out the dough into a 12- x 18-inch rectangle.
For the Filling:
Combine the brown sugar, cinnamon, and pumpkin pie spice in a small bowl. Evenly spread the butter all over the dough using a pastry brush. Sprinkle the brown sugar mixture over the butter.
Starting with one of the long ends, tightly roll the dough from end to end and gently punch the edges together to seal.
Cut the dough into 1 1/2-inch thick sections using a sharp knife or a strand of unscented dental floss. Place rolls 2-inches apart on a lightly greased baking sheet; cover tightly with plastic wrap and let proof in a warm place until puffy, about 45 minutes to 1 hour.**
Meanwhile, preheat the oven to 350°F. Bake 22 to 25 minutes or until the edges are just golden brown.
For the Frosting
Beat the cream cheese and butter in a medium bowl until smooth and fluffy, about 2 minutes. Add the powdered sugar and vanilla and beat until smooth. Spread the frosting over the warm cinnamon rolls.
Notes
*Add more flour, 1 Tbsp at a time, if needed, if you feel the dough is too tacky.**If you're wanting to make overnight cinnamon rolls: after placing rolls 2-inches apart on a greased baking sheet, place them in the refrigerator, covered tightly with plastic wrap, overnight. In the morning, remove them from the refrigerator and let them sit in a warm place for 1 to 2 hours or until slightly puffed. Continue with instructions as stated above.