PREPARING THE DOUGH: Lightly coat a large bowl with vegetable oil and set aside.
Place the peeled potatoes and 1 1/2 cups water in a medium saucepan over medium-high heat. Bring the water to a boil and cook the potatoes until they are easily pierced with a fork -- about 15 minutes. **Important:Drain but reserve the cooking liquid.
Mash the potato and 3/4 cups of the cooking water in a large bowl. Stir in buttermilk, butter, sugar and salt; cool to room temperature. Add the yeast and stir to dissolve. Stir in the flour until a stiff dough forms.
Transfer the dough to a lightly floured work surface and knead until smooth and elastic; about 10 minutes. Shape the dough into a ball, place it in the prepared bowl, cover with a clean damp towel and let rise until doubled in volume for about 1 hour.
SHAPING THE DOUGH: Preheat oven to 375° degrees. Lightly coat the cups of two 12-cup muffin pans with oil and set aside.
Next punch the risen dough down, remove from bowl and knead the dough lightly on a floured surface. Divide the dough into 60 uniform pieces and form each into a small ball. Place 3 balls in each muffin cup, cover with a damp clean towel, and let dough rise until doubled in size, about 1 hour.
Bake until the tops of the clover rolls are golden brown; approximately 30 minutes.