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.