In a small bowl or measuring cup, combine the milk and water. Heat in a microwave until the temperature reaches between 102 and 100 degrees F, about 40 seconds. Stir 1 teaspoon of sugar into the mixture and add the yeast. Gently mix and set aside to allow the yeast to activate and become foamy about 5 minutes.
With a stand mixer fitted with the dough hook attachment, add in the egg, salt, 3 tablespoons butter, sweet potato, and flour and mix until combined, about 2 minutes. Slowly pour in the yeast mixture and allow it to incorporate. Mix until the ingredients are smooth and doughlike, and the dough pulls away from the sides of the bowl but still sticks to the bottom. This will take about 8 minutes. If the dough is still sticking to the sides of the bowl after 8 minutes, add an additional 1/4 cup flour, 1 tablespoon at a time, until the dough releases from the sides.
Roll the dough out onto a lightly floured surface. Knead the dough until it becomes a smooth and uniform ball. Place it into a lightly greased bowl, cover it with plastic wrap and set it in a warm place for about 1 hour or until the dough doubles in size.
Roll the dough out onto a lightly floured surface and cut it into 8 to 10 equal pieces. Roll the dough into small balls, and place them seam-side down in a greased skillet (or one lined with parchment paper). Cover and let rise until rolls have doubled in size.
Preheat your oven to 350 degrees. Bake 20 to 25 minutes or until the rolls are golden brown on top and have reached 200 degreed F internally.
Cool 5 to 10 minutes before enjoying.