Lightly whisk the yeast and ¼ cup warm water in a liquid measuring cup. Let stand for 5 minutes.
1 tablespoon active dry yeast, 1¼ cups water
In the bowl of a stand mixer fitted with the paddle attachment, beat the yeast mixture, remaining 1 cup warm water, 2 cups of flour, eggs, melted shortening, sugar, and salt together. Beat for 2 minutes, or until the mixture starts to form a soft dough.
4½-5 cups all-purpose flour, 3 large eggs, ½ cup vegetable shortening, ½ cup granulated sugar, 5 teaspoons kosher salt
Slowly add enough of the remaining flour (usually about 2½-3 cups more) and mix just until it is incorporated.
Spray (or butter) the inside of a glass bowl with nonstick spray, then place the dough inside, flipping to coat the ball. Cover the bowl, place it in a proofing oven or warm place, and allow the dough to rise (it should double in size) for about 1-1½ hours.
After the dough has risen, punch it down, cover, and refrigerate it for at least 8 hours or overnight.
When ready to make the rolls, remove the dough from the refrigerator, punch it down again, and divide it in half. Cover the dough loosely with plastic wrap to keep it from drying out.
Spray two 9-inch baking pans or cake pans with nonstick spray.
Make the pecan topping while the dough rests on the countertop. In a small medium bowl, whisk the melted butter, granulated sugar, brown sugar, corn syrup, salt, and water together until the mixture is smooth.
12 tablespoons unsalted butter, ¾ cup dark brown sugar, ¾ cup granulated sugar, ½ cup dark corn syrup, 1 teaspoon kosher salt, ¼ cup water
Pour an equal amount of the pecan topping into the prepared pans (about 348 grams per pan). Sprinkle half of the chopped pecans onto the pecan topping (1 cup in each pan).
2 cups chopped pecans
Make the cinnamon sugar filling before rolling out the dough. Melt 1½ cups (3 sticks) of butter in a microwave safe bowl. Set aside. In a medium bowl, whisk the sugars, cinnamon, and pie spice together. Set aside.
1½ cups unsalted butter, 1 cup granulated sugar, 1 cup dark brown sugar, 3 tablespoons ground cinnamon, 2 tablespoons apple pie spice
Place half of the dough on a lightly floured work surface and knead it about 5 times to smooth it out. Roll the dough into a large rectangle, ⅓-inch thick, allowing it to rest periodically until it stops pulling back. Slightly stretch the corners to make an even rectangle about 18x15-inches in size. If the size of the rectangle is smaller, that’s okay - it’s more important the dough is ⅓ inch thick and in a rectangular shape.
Brush 12 tablespoons of melted butter evenly over the dough. Sprinkle with half of the cinnamon-sugar filling, leaving a ½ inch border around the dough without cinnamon sugar.
Beginning at the long edge nearest you, roll the dough (not too tightly) into a cylinder. Pinch the long seam to seal it and position the cylinder so the pinched seam is down. Trim off about ½ inch of dough on each end of the dough cylinder.
Use waxed dental floss to cut the dough into rolls, about 1½ inches thick. To slice with floss, hold a 10-inch length of floss taut and slide it underneath the dough cylinder. Pull up the floss and cross the ends of it over each other and gently pull until the dough is cut through. Repeat. (If you don’t have floss, use a serrated knife and gently saw the dough into rolls.)
Transfer the rolls, cut-side down, to the prepared pan with ½ inch between each roll.
Cover the rolls with plastic wrap and let rise until rolls are puffy, about doubled in size, and touching each other, 45-90 minutes.
Preheat oven to 350°F. Cover a large, rimmed baking sheet with foil and place it on the lowest rack in the oven to catch any drippings.
Once the rolls have risen, remove the plastic wrap and place the rolls in the oven. Bake for 30-35 minutes, or until the internal temperature registers 200°F on an instant-read thermometer. If the buns are browning too quickly, loosely cover with sprayed foil.
Remove from the oven and let the rolls cool for 5 minutes.
Very carefully invert the rolls onto a large serving plate (a plate larger than the baking pans). Be very careful when inverting the rolls - the glaze (at the bottom of each pan) is extremely hot and gooey at this point.
Allow the rolls to cool for about 5-8 minutes before serving.