Instructions

For the soaker: Stir all ingredients in large bowl with wooden spoon until shaggy mass forms. Transfer dough to lightly floured counter and knead by hand until smooth, about 3 minutes. Return soaker to bowl, cover tightly with plastic wrap, and refrigerate for at least 8 hours or up to 24 hours.
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: Tear soaker into 1‑inch pieces and place in bowl of stand mixer fitted with dough hook. Add sponge, flour, butter, honey, yeast, oil, and 2 teaspoons salt and mix on low speed until cohesive dough starts to form, about 2 minutes, scraping down bowl as needed. Increase speed to medium-​low and knead until dough is smooth and elastic and clears sides of bowl, about 8 minutes.
Transfer dough to lightly floured counter and knead by hand to form smooth, round ball, about 30 seconds. Place dough seam side down in lightly greased large bowl or container, cover tightly with plastic wrap, and let rise until doubled in size, 1 to 1½ hours.
Lightly flour 2 parchment paper–lined rimmed baking sheets. Press down on dough to deflate. Transfer dough to lightly floured counter; stretch and roll into even 12‑inch log. Cut log into 8 equal pieces (about 4 ounces or 113 grams each) and cover loosely with greased plastic. Working with 1 piece of dough at a time (keep remaining pieces covered), pat into 4‑inch disk. Working around circumference of dough, fold edges of dough toward center until ball forms. Flip dough ball seam side down and, using your cupped hand, drag in small circles until dough feels taut and round and all seams are secured on underside of ball.
Arrange buns seam side down on prepared sheets, spaced evenly apart. Cover loosely with greased plastic and let rise until nearly doubled in size and dough springs back minimally when poked gently with your knuckle, about 1 hour.
Adjust oven racks to upper­-middle and lower-middle positions and heat oven to 350 degrees. Lightly beat egg, water, and remaining pinch salt together in bowl. Gently brush buns with egg mixture. Bake until golden brown, 18 to 22 minutes, switching and rotating sheets ­halfway through baking. Transfer buns to wire rack and let cool completely, about 1 hour, before serving. (Cooled buns can be stored in zipper-lock bag at room temperature for up to 2 days. Wrapped in aluminum foil before being placed in bag, buns can be frozen for up to 1 month. To reheat thawed, frozen buns, place them on rimmed baking sheet, still in foil, and bake in 350‑degree oven for 10 minutes.)