Makes 30 to 35 rolls.
2 small russet potatoes, peeled and cut into 2-inch pieces
2 packages active dry yeast
2 tablespoons sugar, plus a pinch
1 cup buttermilk, room temperature
6 tablespoons butter, melted and cooled, plus more for bowl and plastic wrap
4 teaspoons coarse salt
5 1/2 cups to 6 1/2 cups bread flour, plus more for dusting
1. Place potatoes in a medium saucepan; cover with cold water. Bring water to a boil; reduce to a simmer. Cook potatoes until knife-tender, about 15 minutes. Drain, reserving 1/2 cup of the liquid. Mash potatoes; set aside.
2. Cool reserved liquid to 105 degrees. In the detached bowl of an electric mixer, whisk liquid, yeast, and pinch of sugar. Set aside until mixture is foamy, about 10 minutes.
3. Attach bowl to electric mixer fitted with the dough-hook attachment. With the mixer on low, add remaining sugar, reserved potatoes, buttermilk, 4 tablespoons melted butter, and salt. Gradually add enough flour to make a slightly sticky dough. Knead dough until smooth, about 2 minutes. Brush a mixing bowl with butter. Place dough in bowl; cover bowl with buttered plastic wrap. Set aside to rise until doubled, 1 to 1 1/2 hours.
4. Heat oven to 375 degrees. Line 3 large baking sheets with parchment. Turn dough out onto a floured work surface. Using a floured rolling pin, roll dough out 3/4 inch thick. Cut dough into 2-inch-wide strips. Cut strips into triangles or squares; place at least 1 1/4 inches apart on baking sheets. Brush tops with remaining melted butter; cover with buttered plastic wrap. Let rise until dough does not spring back when pressed with a finger, 15 minutes. Bake until golden, 18 to 20 minutes; serve.