Add the sugar, salt, eggs and 1 cup of flour to the bowl with the yeast mixture. Using a dough hook, run the heavy duty mixer on low speed for about a minute until the mixture is just about incorporated. Add the remaining half cup of flour and run the mixer in medium speed. Continue to beat, scraping the bowl as needed, for about 15-20 minutes. You will know when the dough is ready if it is coming together in the center of the bowl, and also attaching itself into the dough hook. You should see the dough slapping the sides of the bowl, like it is almost violently throwing itself to the sides white it still clinging and rotating with the dough hook. You should also hear the slapping sounds.
Now add the butter bit by bit. Make sure that the butter is in in room temperature, but not warm or oily. When you add the butter, the dough will fall apart again for a moment. Continue to beat until you hear the slapping sounds again. This should take about 5 minutes or so. The dough is now , once again, clinging together in the center and in the dough hook with the slapping sound. Dough is sticky but shiny at this point.
After the dough has doubled in size, gently deflate it by lifting and then letting it fall back to the bowl. Cover the bowl again with a plastic wrap and chill in the refrigerator for 6 hours or overnight. The dough will double in size again ( After the long chill, you can now divide the dough in half. Use 1/2 for the sticky buns and reserve the other half for future use. You can freeze the dough for up to three weeks, tightly wrapped in plastic and foil).
In a small bowl, add raisins, 1/4 cup boiling water and 2 tbsp. dark rum. Cover and let stand for at least 1 hour. Meanwhile, combine sugars, cinnamon and pecan on another bowl. When ready to roll the dough, drain the raisins and set aside the soaking liquid.
Stir together softened butter, sugar, and corn syrup until everything is incorporated. Spread this mixture evenly on a greased 8 x 2 square baking pan.
Reserve about 4 tablespoon of the soaking liquid of the raisins and stir in melted butter.
In a floured surface, roll the dough to a 14 x 12 inch rectangle. Brush the surface with beaten egg using a pastry brush. Sprinkle the cinnamon sugar mixture and the raisins all over the dough. Use your hands to spread it evenly. Roll the dough into a log starting on the long side. Press the seams to seal the dough. Cut the dough into 4 equal portions, then cut each portion to three equal portion to yield 12 cut rolls.
Place 2-3 pieces of pecans on each of the cut end of the rolls, pressing them firmly to adhere. Place each roll with the pecan side down on the prepared baking pan. Space them evenly and when all rolls are positioned, press them down so they are more plump and their sides are touching.
Let the rolls rise, covered loosely with plastic wrap for 2 hours. Place an oven rack in the lowest position of the oven. Pre-heat oven to 425 F ( 400 F if you are using a dark pan). Brush the surface of the rolls with the glaze using a pastry brush. Set the baking dish on top of a baking sheet and place in the lowest rack of the oven. Bake for 10 minutes then lower the temperature to 375 F. Bake the rolls for another 12-15 minutes or until the buns are lightly golden. To prevent over-browning, cover the buns loosely with foil after the first 7 minutes (during the 375 F stage).
Let the buns cool slightly for a minute or two then turn it over on a serving plate. Sticky buns should be stored in a tightly covered container at room temperature. Re-heat leftovers in the microwave for 10-20 seconds.
Preparation times does not include chilling and rising times for the dough.