Add 1 cup bread flour and 2/3 cup active potato flake sourdough starter to a large mixing bowl. Mix with a silicone spatula until combined.
Cover tightly and allow the preferment to rest at room temperature for 8–24 hours. It may become fluffy and increase in size, but it may or may not double.
After the preferment has fermented, add 1/2 cup warm water, 1/2 cup active potato flake sourdough starter, and 2 1/2 cups bread flour.
Gently mix with a silicone spatula or wooden spoon until all of the flour has been moistened and no dry pockets remain. If needed, lightly oil your hands and gently work the dough together in the bowl. The dough should be wet and sticky.
Cover and allow the dough to rest for 30 minutes.
Add 1 1/2 teaspoons salt during the first set of stretch-and-folds. With lightly oiled hands, stretch one side of the dough upward and fold it over to the opposite side. Rotate the bowl 90 degrees and repeat. Continue until you have gone around the bowl twice, for approximately 8 folds.
Cover and rest for 30 minutes.
Repeat the stretch-and-fold process three more times, resting the dough for 30 minutes between each set. Complete a total of four sets of stretch-and-folds.
After the final stretch-and-fold, cover the dough and allow it to ferment at room temperature for approximately 4–5 hours.
Transfer the covered dough to the refrigerator for at least 10 hours and up to 24 hours.
After the extended fermentation, lay out a piece of parchment paper that will fit your baking sheet or baking stone and generously flour it.
Using lightly oiled hands or a lightly oiled spatula, gently scrape the dough onto the floured parchment. Generously flour the top of the dough.
Using floured hands, gently stretch the dough into a rough 10×7-inch rectangle, being careful not to significantly deflate it.
For 8 rectangular rolls, use a floured bench scraper to divide the dough into 8 approximately equal pieces, roughly 2.5×3.5 inches each.
For 12 smaller square rolls, divide the dough into 12 approximately equal pieces using a 3×4 grid.
Arrange the rolls at least 2 inches apart on the parchment paper. Handle them gently and avoid pressing out the air.
Lightly sprinkle flour over the rolls and gently cover with a clean kitchen towel or parchment paper.
Allow the shaped rolls to proof at room temperature for 3 hours.
Approximately 40 minutes before baking, position one oven rack on the lowest level and another in the center. Place a baking sheet or baking stone on the center rack and preheat the oven to 450°F.
When ready to bake, place several cups of ice in a shallow metal roasting pan, cast-iron skillet, or rimmed metal baking sheet. Do not use glass.
Uncover the rolls. If desired, lightly spray or flick the tops with a little water for additional steam.
Working quickly, transfer the parchment paper and proofed rolls onto the preheated baking sheet or baking stone. A pizza peel makes this especially easy.
Place the pan of ice on the bottom oven rack and quickly close the oven door to trap the steam.
Bake at 450°F for 20–22 minutes, or until golden brown. Bake up to approximately 25 minutes for a deeper golden color.
The finished rolls should sound hollow when tapped. For a more accurate test, the internal temperature should reach approximately 200–205°F.
Transfer the rolls to a cooling rack and allow them to cool for at least 45 minutes before slicing.