Peel and dice your sweet potato. Weigh and place about 250g into a small pot with cold water. If you have +/- 10g this recipe will still work fine.
Boil your potato until it is fork tender (10-15 minutes). Remove from heat, mash until very smooth. Let cool until lukewarm/room temperature.
In the bowl of your stand mixer with dough hook attached, combine all your dough ingredients except for the 2 tbsp of softened butter. Mix until dough comes together. Dough can still have dry spots but it will have formed a rough ball.
Add butter 1 tbsp at a time, waiting until the first is fully incorporated before second is added.
Knead dough for 5-8 minutes until dough is smooth and stretchy. It will still be a little sticky.
Place dough in a lightly greased bowl, cover and let rise in a warm area for 1-2 hours. Dough will have at least doubled in size.
Line a 13x9 baking pan with parchment paper.
Remove dough onto a lightly floured or greased counter and divide into 12 equal portions.
Taking each dough piece one at a time, shape into a ball and cup hand over dough on counter and make circular motions to create a uniform ball with tension. Place into pan and repeat with the rest of the remaining dough.
Cover the dough and allow to rise for another 45 minutes to an hour. Dough will be puffy and about twice the size.
About 30 minutes into proofing, preheat oven to 350°F.
Bake rolls for about 25 minutes on center rack. Rolls are done with the tops are beginning to be golden brown.
While rolls are warm, whisk together brown sugar and 1 tbsp melted butter. Use a pastry brush and brush the tops of the rolls.
Rolls can be eaten right away, or stored in an airtight container for about 3 days.