Boil potato in a small saucepan of boiling water (no need to add salt) until a paring knife passes through flesh with no resistance, 30–40 minutes; drain. When cool enough to handle, pass through ricer into a small bowl (peel won’t go through; discard peels). 1 6 ounce medium Yukon Gold potato
Mix milk and ¾ cup riced potato in the bowl of a stand mixer with whisk or whisk attachment until no lumps remain.
1 cup whole milk
Add ½ cup melted butter and mix until incorporated.
½ cup unsalted butter
Switch to dough hook. Add all-purpose flour, yeast, and sugar and mix on medium speed, scraping bottom and sides of bowl as needed, until a very wet, sticky dough forms, about 2 minutes.
1 ½ cups all-purpose flour, 2 ¼-ounce envelopes * active dry yeast, 3 heaping tablespoons granulated sugar
Let dough rise, uncovered, in a warm spot, 30 minutes (it will have puffed slightly). Pro Tip: If your kitchen is cold, I recommend placing the dough in a cold oven with just the light on. This creates just enough warmth to allow the dough to rise well.
To the dough, add eggs, egg yolk, 2 ⅔ cups bread flour, and 1 tablespoon kosher salt and mix on medium-high with dough hook, adding more bread flour if needed if dough is sticking to sides of the bowl, until dough is smooth and elastic and pulling away from the sides of the bowl, about 5 minutes.
2 large eggs, 1 large egg yolk, 2 ⅔ cups bread flour, 1 tablespoon kosher salt
Brush surface of dough with melted butter, cover, and let rise in a warm spot 30 minutes (dough should rise 1½ times its initial size).
¼ cup unsalted butter
Turn out dough onto a lightly oiled surface (I use vegetable oil) and divide into 18 pieces. Pro Tip: To get dough balls that are all the same size, I recommend weighing the dough on a kitchen scale then dividing the total weight by 18. Weigh each piece, breaking off more or less dough, to achieve the correct measurement. Roll each into a ball by cupping your hand around the dough ball in the shape of a letter C, with your pinky finger against the counter and your thumb and forefinger on top of the ball. Circle your hand quickly around the dough while keeping your hand on the counter to form the dough into a smooth ball. Brush a 13x9 inch baking dish with butter and place balls side by side in dish in 6 rows of 3 (rolls will be touching).
Brush tops with more melted butter. Let sit, uncovered, in a warm spot 1 hour.
¼ cup unsalted butter
Preheat oven to 400°F. Carefully and gently brush dough again with melted butter and sprinkle with flaky salt. Bake rolls until deep golden brown, 15–20 minutes. Transfer dish to a wire rack and let rolls cool in dish 10 minutes. Turn out rolls onto rack and let cool 30 minutes before serving.
¼ cup unsalted butter, 1 tablespoon flaky sea salt