For the dough: Place the yeast and 1 cup lukewarm water in the bowl of a stand mixer and whisk to combine. Fit the mixer with the dough hook and add the flour, butter, granulated sugar, salt and egg. Knead on medium-low speed until the dough forms a ball and releases easily from the sides of the bowl, about 4 minutes.
Butter a large bowl; transfer the dough to the bowl. Cover with a towel and set aside in a warm, draft-free place until the dough has doubled in size, about 1 1/2 hours.
Preheat the oven to 375 degrees F. Butter a 9-by-13-inch baking dish.
For the filling: In a medium bowl, stir together the pecans, brown sugar, cinnamon, salt and butter. Set aside.
Punch down the dough, then roll or press it into a 16-by-12-inch rectangle on a lightly floured surface. Spread with the filling, leaving a 1/2-inch border.
Starting at one of the short ends, roll the dough into a cylinder and then slice into 12 rolls. Arrange the rolls, cut-side up, in four rows in the prepared baking dish. Cover with a clean kitchen towel and leave to rise in a warm, draft-free spot until nearly doubled in volume, about 45 minutes. Uncover and bake until golden on top, about 20 minutes.
For the thick cream cheese icing: Blend the cream cheese and confectioners' sugar in a stand mixer fitted with the paddle attachment. Add the milk and mix until smooth. Top the warm cinnamon buns with icing and serve.