Preheat oven to 350* degrees F. In a small bowl or Pyrex measuring cup, microwave the butter and milk on high heat for one minute. Stir, then heat for another 30 seconds. Stir again, and heat for another 30 seconds or until butter is mostly melted and liquid is hot to the touch. Set aside briefly, for about a minute or two to cool or until it's warm but not hot.
In the bowl of a stand mixer, whisk together the milk mixture and the yeast until combined. Add in the sugar, egg, and THREE (3) cups of the flour with the dough hook on medium speed. Turn the speed to medium-high and gradually add in the remaining 1/2 cup of flour or until the dough begins to form a ball at the center of the mixer bowl. Beat for 5 minutes, then remove the dough hook and cover the bowl with a damp cloth for 10 minutes.
While the dough rises, make your sticky caramel sauce. In a small saucepan, combine the brown sugar, butter, corn syrup and vanilla. Bring to a boil over medium-low heat, then stir in the pecans. Remove from heat and set aside.
Lightly dust a flat work space with flour. Roll out the dough into a large rectangle. I don't have dimensions as I just eyeballed it, but you want it to be at least 1/2" to 3/4" thick. Spread the softened butter over the plane of dough, then evenly top with the brown sugar and cinnamon mixture, patting it gently into the dough.
Beginning with the left side, begin tightly rolling the dough into a log. Move the log toward you so you're facing it horizontally. Using flavorless dental floss, begin cutting the dough into 12 evenly sized pieces. Spray a 13x9" baking dish liberally with cooking spray and spread the sticky caramel sauce all over the bottom, evenly spacing the pecans if needed. Top the sauce with the cinnamon rolls in 4 rows of 3 rolls. Cover with a damp cloth and place on top of the oven to rise for 25 minutes.
Once rolls have risen, bake for approx. 15-20 minutes or until rolls are puffy, lightly golden and bubbly. Remove from heat and let cool for 5 minutes - no longer - before carefully and quickly inverting the rolls onto a plate or dish. Rolls are best when they're hot or warm. To eat later, reheat briefly to help loosen the sticky caramel sauce. Store leftovers airtight at room temperature.