DOUGH: In a small saucepan, warm the milk over low heat until it reaches 95-100 degrees. Pour the warm milk into the bowl of a standing electric mixer fitted with the dough hook and stir in the sugar and yeast. Let stand until the yeast is foamy, about 5 minutes.
On low speed, add the softened butter, eggs, and sea salt. Add flour a cup at a time, beating at medium speed until a soft dough forms, about 3 minutes. Increase the speed to medium-high and beat until the dough is soft and supple, about 5 minutes longer.
Form the dough into a ball and transfer it to a large lightly buttered bowl. Cover the dough with plastic wrap and a tea towel, let stand in a warm place until doubled in size about 1 to 2 hours.
APPLE FILLING: While dough is rising, make the filling. Heat 4 tablespoons of the butter and 1/2 cup sugar in a large skillet, then add the apples. Sauté until apples just begin to caramelized. (Do not over-cook or you will have applesauce.) Remove from heat and set aside to cool.
In a small bowl, stir together the brown sugar and cinnamon; set aside.
Line the bottom of a 9 x 13-inch baking pan with parchment paper, allowing the paper to extend up the short sides. Butter the paper and sides of the pan; set aside.
When dough has risen, remove the cover, and punch the dough down with your fist. Turn the dough out onto a lightly floured work surface. Using a rolling pin, roll the dough into a 10 x 24-inch rectangle.
Spread the remaining 2 tablespoons butter out to the edges. Sprinkle the brown sugar/cinnamon mixture evenly over the butter. Spread the apple filling over the brown sugar/cinnamon mixture. Tightly roll up the dough to form a 24-inch-long log.
Cut the log into quarters. Cut each quarter into 4 slices (1 1/2-inches each) and arrange them in the prepared baking pan. (15 rolls will fit in the pan, you will have 1 roll left over) Cover the rolls and let them rise in a warm place until they are puffy and have filled the baking pan, about 2 hours.
Preheat the oven to 425 degrees. Bake the rolls for about 20-25 minutes, until they are golden and the apple filling is bubbling. Transfer the pan to a rack to cool for 30 minutes. Meanwhile, prepare glaze.
CINNAMON GLAZE: In a small bowl, beat the confectioners' sugar and cinnamon with the butter and heavy cream until the glaze is thick and spreadable. Dollop glaze over each roll and spread with an offset spatula. Serve warm or at room temperature.