Grease two baking sheets. Set aside.
In a saucepan of boiling water, cover and cook sweet potato until tender, about 15 minutes. Drain, reserving 1 cup of the cooking liquid. Cool potato and cooking liquid to lukewarm. Peel and mash potato. Set aside.
In large bowl, dissolve suger in warm milk and reserved cooking liquid. Sprinkle in yeast. Let stand until frothy, about 10 minutes.
Stir in mashed potato, green onions, 1 tsp of the cooled butter, 1 cup of the flour and salt to make a smooth paste. Stir in 3 cups of the remaining flour, 1 cup at a time, to make a soft, sticky dough.
Turn out dough onto lightly floured surface; knead until dough is smooth and sticky, adding enough of the remaining flour as necessary. This should take about 10 minutes.
Place in a greased bowl, turning to grease all over. Cover with a warm moist towel and let rise in a warm, draft-free place until doubled in size, about 1 hour.
Punch down dough; turn out onto a floured surface. Divide in half. Roll out each piece to about 1/3 inch thickness. Cut into individual 3 1/2" rounds. Stretch each round into slight ovals; fold crosswise in half and pat tops gently to maintain shape. They should look like little half moons. Place one inch apart on greased cookie sheet. Cover again and let rise in a warm draft free place for about 40 minutes.
Brush tops with butter.
Bake one sheet at a time, in center oven at 400°F The rolls will be golden and will sound hollow when tapped on the bottom, about 15-18 minutes.