Cook sweet potatoes in a kettle of water just to cover. When easily pierced with the tip of a sharp knife, about 30 minutes, remove potatoes from water; reserve 1/2 cup of water. Peel potatoes and mash by hand; don't purée them. Set aside.
When mashed potatoes are just lukewarm, place them in a large bowl. Add egg, honey, butter and salt; mix well.
In a separate bowl, dissolve yeast in lukewarm potato cooking water. When yeast has dissolved and is beginning to foam (about 10 minutes), add to potato mixture. Stir in just enough flour to make a soft dough. Turn dough onto floured work surface and knea
Next day, remove dough from refrigerator and let it come to room temperature, about 2 hours. Punch dough down, knead for 1 minute, then let rest, covered with a damp cloth, for 10 minutes.
Divide dough into 36 pieces. Roll each piece into a ball. Grease 12 muffin cups, and place three balls in each cup. Let rise until doubled in bulk, about 1 hour.
Gently brush buns with egg white glaze. Bake in a preheated 400°F oven until buns are golden brown, about 20 minutes. Remove buns from pan and cool slightly on a wire rack; serve warm.