Pour warm milk for the dough into the bowl of an electric stand mixer fitted with the dough hook and stir in the sugar and yeast. Let rest for about 5 minutes until the yeast is foamy. Add the softened stick of butter, eggs, sea salt and chai spice. Beat to combine. Then add the flour and beat until a soft dough forms on medium speed, approximately 3 minutes. Increase speed to high and beat until the dough is soft and pliable, an additional 10 minutes.

Remove the dough and place on a lightly floured surface. Knead with your hands a few times and then form the dough into a ball. Grease a medium size bowl with butter and add the dough ball to the bowl. Cover with plastic wrap and let rest in a warm place until doubled in size, about 1 1/2 to 2 hours.

Line the bottom of a 9x13-inch baking pan with parchment paper, allowing the paper to extend up the long sides. Grease the paper with butter. Turn out the dough from the bowl onto a lightly floured work surface and roll out into a 10"x24" rectangle.

In a small bowl, whisk together brown sugar, ground chai spice, and pumpkin pie spice for filling.

Spread the rectangle of dough with butter for filling. Sprinkle the sugar spice mixture on top.

Tightly roll the dough to form a 24-inch log. Cut the log into quarters and then cut each quarter into 4 slices. Arrange the slices in the baking pan with the cut sides up. Cover the rolls with plastic wrap and allow them to rise for an additional 2 hours.

Preheat the oven to 425 degrees. Bake the rolls for about 20 minutes, until they are golden brown. Transfer the pan to a rack and allow to cool for 30 minutes.

In a small bowl, whisk together the confectioners' sugar, butter, heavy cream, cream cheese, and pumpkin pie spice until the frosting is spreadable.

Grab the sides of the parchment paper that hang over the baking pan and invert the rolls onto a cooling rack. Peel off the parchment paper off and turn the rolls over onto a serving platter. Spread frosting evenly over the rolls with a spatula. Serve immediately.