In a large bowl, combine yeast, white sugar, and warm water. Stir together and let stand for 5 minutes or until foamy.
Add brown sugar, mashed sweet potatoes, softened butter, eggs, and salt to the bowl. Stir using a wooden spoon to incorporate the ingredients.
Add 3 cups of the flour and stir the dough until flour is moistened.
Stir the mixture until a soft, sticky dough forms and gathers at the center of the bowl, sprinkling in the remaining ½ cup flour as needed to help manage the stickiness.
Generously flour a working surface as well as your hands. Turn the dough over and knead it until it is smooth. Add more flour as needed to prevent the dough from sticking to hands and to the working surface.
Once the dough is manageable, stop adding the flour. Continue to knead just until the dough is smooth but still slightly sticky.
Shape the dough into a ball and place in an oiled bowl. Cover and let rise for about an hour, until doubled in size.
Once the dough has risen, punch it down and divide into 16-20 portions.
Shape each piece into a smooth ball and place on a greased 9×13 baking sheet. Cover the rolls loosely with plastic or a clean kitchen towel.
Let rise for 40 to 60 minutes or until puffy and have doubled in size. Bake in a 375 F oven for about 12 to 16 minutes or until the tops are golden.
To test if the dough has been kneaded enough, take a small portion of dough and using fingers, stretch it out into a little square. A translucent film should form in the center before it tears.