To make the dough: Place yeast and sugar into a stand mixer with the dough hook attached. Add the warm water and gently stir. Let sit until yeast has doubled and is puffed and foamy on top, about 10 minutes.
To the bowl add the melted butter, warm milk, sweet potato puree and egg, stir to combine. Add in the flour, nutmeg and salt. Knead the dough with the dough hook until the dough is smooth and forms a ball, about 5 minutes. Remove the dough from the bowl and oil the bowl or use cooking spray. Place the dough back in the bowl and cover with plastic wrap. Let the dough rise in a warm area for about 1 hour or until doubled in size.
To make the filling: Add the sugar and cinnamon to a bowl and mix well. Generously grease a 9×13 inch baking dish (may also use a slightly smaller baking dish) with butter.
Lightly dust a surface with flour. Roll the dough into a rectangle (about 9×24 inches). Spread about 6 tablespoons of the butter (softened almost to a melted stage) evenly over the dough. Spread the cinnamon sugar evenly over the butter and lightly push the cinnamon sugar into the butter.
Starting with the long edge closest to you, carefully roll the dough into a log, keeping it fairly tight as you go. When you reach the edge, pinch along the edge to seal. Place dental floss or a thin piece of string (do it! it works so well!) under the roll where you want to cut. Mine are usually about 3/4 to 1 inch thick, but vary. Take the ends of the floss in each hand and wrap them around the roll. Keeping the ends of the floss in each hand (don’t let go) tighten the floss so it starts to cut through the roll. Again, don’t change hands. Tighten until the floss comes out and the individual roll is separated. You can make eight larger rolls OR 10-12 smaller rolls.
Place rolls in the prepared pan. Cover with a damp cloth or plastic wrap and allow to rise in a warm place until doubled in size, about 30 minutes.
Preheat oven to 350. Just before baking brush the remaining 2 tablespoons butter on top of the rolls. Bake the rolls for 25 minutes or until golden brown.
Meanwhile, make the frosting. Bring a large pot (big enough to place your mixing bowl over top) of water to boil. In the bowl of a stand mixer whisk the egg whites and sugar together. Place the bowl of the stand mixer over the pot of boiling water and cook, stirring often, until the egg whites are very warm to the touch and the sugar has dissolved, remove the bowl from the heat. Whip the egg whites on high until stiff peaks form. Allow the egg whites to cool slightly before continuing.
Once cool, add the butter, vanilla and salt. Beat until combined and fluffy, making sure not to overbeat. Spread the frosting on warm rolls.
Sprinkle with toasted pecans. EAT!