Mix warm water with the granulated sugar in a small bowl, sprinkle the yeast in the bowl and let it bloom for 10 - 15 minutes.
Simmer the milk and butter in a small sauce pan until the butter is completely melted. Let cool to room temperature or at least just around 100°F.
Wash the sweet potato and pierce with a pairing knife a few times. Wrap it in plastic and microwave for 6-8 minutes until tender. Check by poking it with a knife or fork, if it goes through easily, your potato is done.
Let the potato cool on the counter until you can handle it without burning your hand.
Cut open the potato and scoop out the flesh, smash it in a small bowl with a potato smasher.
Add flour, brown sugar, cinnamon and salt in a medium bowl and mix well with a whisk.
In the bowl of your stand-mixer, add 1 cup of mashed sweet potato and the warm milk/butter mixture, mix with a whisk to combine.
Check the temperature of the liquid mixture to make sure it is not more than 110°F to ensure a safe temperature for the yeast.
Now add the flour mixture along with the activated yeast to the liquid mixture in the stand-mixer bowl.
Knead with the dough hook on medium speed for 1-2 minutes just until the dough starts to come away from the side of the bowl.
Turn dough out on a lightly floured counter, shape into a ball, put it back into the bowl and allow to rise at room temperature overnight or until double in size, this may take a few hours or longer.
The next day, or when the dough has risen enough, turn it out on a lightly floured counter again. If the dough stick the the side of the bowl, just use a scraper to get it all out.
Divide dough into 2 ounce portions and shape them into round balls. This batch will make about 18.
Place the dough balls on parchment line baking sheets about 2 inches apart and let them rise for about 2 hours or until at least double in size. You may need 2 or more baking sheets.
Prepare egg wash by beating one egg with 1 tablespoon of water.
Brush the top of the risen dough with egg wash very lightly.
Preheat oven to 400°F, and bake for 15 minutes until golden brown.
Remove from oven and let cool on a wire rack.
Serve rolls warm with butter.