Instructions

For the sponge: Stir all ingredients in 4‑cup liquid measuring cup with wooden spoon until well combined. Cover tightly with plastic wrap and let sit at room temperature until sponge has risen and begins to collapse, about 6 hours (sponge can sit at room temperature for up to 24 hours).
For the dough: Whisk flour, 1½ teaspoons salt, and yeast together in bowl of stand mixer. Stir ¾ cup water and milk into sponge with wooden spoon until well combined. Using paddle on low speed, slowly add sponge mixture to flour mixture and mix until cohesive dough starts to form and no dry flour remains, about 2 minutes, scraping down bowl as needed. Increase speed to medium-​low and continue to mix until dough becomes uniform mass that collects on paddle and pulls away from sides of bowl, 4 to 6 minutes.
Remove paddle and fit stand mixer with dough hook. Knead on medium-low speed until dough is smooth and shiny (dough will be very sticky), about 10 minutes. Transfer dough to lightly greased large bowl or container, cover tightly with plastic, and let rise until doubled in size, 30 minutes to 1 hour.
Using greased bowl scraper (or rubber spatula), fold dough over itself by gently lifting and folding edge of dough toward middle. Turn bowl 45 degrees and fold dough again; repeat turning bowl and folding dough 6 more times (total of 8 folds). Cover tightly with plastic and let rise for 30 minutes. Repeat folding, then cover bowl tightly with plastic and let dough rise until nearly doubled in size, about 30 minutes.
Lightly flour 2 parchment paper–lined rimmed baking sheets. Transfer dough to well-floured counter. Dust top of dough with flour, divide into 2 equal pieces, and cover loosely with plastic. Using your well-floured hands, press and stretch one piece of dough into 8 by 8‑inch square (keep second piece of dough covered). Using pizza cutter or bench scraper, cut dough square into quarters (­forming four 4 by 4‑inch squares). Gently brush excess flour from top of each square. Fold four corners of each square into center to form rough 3½‑inch round and pinch edges to seal. Repeat with second piece of dough.
Arrange rolls seam side down on prepared sheets, spaced evenly apart. Cover loosely with greased plastic and let rise until puffy and surfaces develop small bubbles, about 45 minutes.
Adjust oven racks to upper-middle and lower-­middle positions and heat oven to 450 degrees. Lightly beat egg, remaining pinch salt, and remaining 1 tablespoon water together in bowl. Gently brush rolls with egg mixture and bake until golden brown, 13 to 17 minutes, switching and rotating sheets halfway through baking. Transfer rolls to wire rack and let cool completely, about 1 hour, before serving. (Cooled rolls can be stored in zipper-lock bag at room temperature for up to 2 days. Wrapped in aluminum foil before being placed in bag, rolls can be frozen for up to 1 month. To reheat thawed, frozen rolls, place them on rimmed baking sheet, still in foil, and bake in 350‑degree oven for 10 minutes.)