Combine the warmed milk, instant yeast, and sugar in the bowl of a stand mixer fitted with a dough hook (or a large mixing bowl). Add the flour, mashed potatoes, sourdough discard, beaten egg, and salt. With the mixer on low, slowly pour in 2 Tablespoons of melted butter. Increase speed to medium and mix until a rough dough forms, about 2 minutes.
Transfer the dough to a smooth work surface and knead until smooth, about 3-4 minutes. The dough should be completely smooth, soft, and may be slightly tacky but not sticky. If needed, add more flour or milk (1 teaspoon at a time) to reach your desired consistency.
Transfer the dough to a large oiled bowl and cover with plastic wrap. Let rise for 90 minutes, or until doubled in size.
Brush a 9x13-inch baking pan with 1 Tablespoon melted butter and set aside.
Turn the dough onto a smooth work surface and divide into 15 equal-sized pieces using a kitchen scale. First, weigh the dough on the scale and divide that number by 15. For me, each roll weighs about 73 grams.Using one palm for friction, roll each piece of dough into a ball, then place the rolls seam-side down in the prepared baking pan. Repeat until you have 15 rolls.
Cover the baking pan with plastic wrap and let the rolls rise for 60 minutes, until puffed and doubled in size.
Preheat the oven to 375℉. Brush the rolls with 2 Tablespoons melted butter, then sprinkle with flaky sea salt. Bake for 25-28 minutes until golden brown. If desired, brush with additional melted butter before serving.
Video
Notes
*I recommend using russet potatoes for their high starch and low water content. Boil and mash one russet potato for this recipe. Mash the potatoes until smooth (not chunky) for the best result. Also, warming the mashed potatoes helps the dough to rise quicker. If you want to use leftover mashed potatoes, you can! Since they likely have milk, butter, salt and pepper in them, you can decrease the amount of added salt in the recipe. You may also need to increase the amount of flour as you're kneading to reach the desired dough consistency. To make these rolls with active sourdough starter, omit the yeast and replace the sourdough discard with active starter (200g). You will also need to increase the rise times.