Combine yeast with warm water (95F to 115F) and 1/2 teaspoon sugar in a small bowl and stir to combine. Let stand for 15 minutes or until yeast has proofed and is bubbly.
Add warm milk, melted butter, remaining 1/2 cup sugar, sweet potato, and 1 teaspoon salt to the bowl of a stand mixer. Mix for a minute or two on LOW speed (speed 2 on the KitchenAid) until well combined. Add 2 cups of flour and mix again to combine. Add lightly beaten eggs and the proofed yeast mixture and beat on MEDIUM speed (speed 4 on the KitchenAid) for a couple of minutes until smooth. Add in just enough of the remaining 2-1/2 to 2-3/4 cups flour, until the dough comes together but is still very thin and sticky.
Replace the paddle attachment with the dough hook and set the mixer on LOW speed and continue to mix for 3 to 4 minutes, until smooth. A good portion of the dough should begin to cling to the dough hook. If it is too thin, add a very small amount of flour, in increments, until it does. Some of the dough will still be at the bottom of the bowl.
Pull the sticky dough together with floured hands and transfer it to a floured board. Work in just enough of the remaining flour until the dough is smooth and elastic and you are able to form it into a soft ball. It will still be quite sticky.
Place the dough ball in a large bowl that you've greased with softened butter or non-stick cooking spray and turn once to grease the surface of the dough. Cover and let rise in a warm place until doubled in size (about 1 hour).
Meanwhile, coat a 12" x 17" rimmed baking sheet or two 13" x 9" baking dishes with non-stick cooking spray. If your baking sheet is dark I highly recommend lining it with parchment paper instead to avoid over-browning the rolls.
Punch the dough down to deflate it and transfer it to a floured cutting board. Use a sharp knife to divide the dough into 4 equal pieces, pinch off 6 equal sized pieces from each quarter of dough (for 24 rolls in total), roll them into smooth balls, and transfer them to the prepared rimmed baking sheet (or baking dishes). Cover with clean kitchen towel(s) and allow the rolls to rest in a warm place for about an hour for their second rise.
Preheat oven to 375 degrees F. Bake the rolls for about 16 to 18 minutes or until golden brown. If you are using a metal baking sheet I recommend rotating it halfway through the baking time to ensure even browning. Remove from oven and brush with melted butter. Serve warm.