3/4 cup warm water
3 tablespoons warm milk
2 teaspoons active dry yeast
2 ½ tablespoons sugar
3 large eggs (2 for dough, one of egg wash)
3 cups bread flour
⅓ cup all-purpose flour
2 tablespoons Hot Crispy Oil
1 ½ teaspoons salt
2 ½ tablespoons unsalted butter, softened
In a glass measuring cup, combine warm water, milk, yeast and sugar. Let stand until foamy, about 5 minutes. Meanwhile, beat 2 eggs.
In a bowl of stand mixer with dough hook attachment, whisk flours with salt. Add butter and turn on mixer until dough hook has combined evenly through flour. Add in yeast mixture, Hot Crispy Oil and beaten eggs until a dough forms. Scrape dough onto lightly floured counter and knead until smooth and elastic, 8 to 10 minutes.
Shape dough into a ball and return it to an oiled bowl. Cover bowl loosely with a towel and let rise in a warm place until doubled in bulk, 1 to 2 hours.
Line a baking sheet with parchment paper. Using dough scraper, divide dough into 8 equal parts. Gently roll each into a ball and arrange 2 to 3 inches apart on baking sheet.
Cover loosely with a clean kitchen towel and let buns rise in a warm place for 1 to 2 hours.
Set a large shallow pan of water on oven floor. Preheat oven to 400 degrees with rack in center. Beat remaining egg with 1 tablespoon water and brush some on top of buns. Bake, turning sheet halfway through baking, until tops are golden brown, about 15 minutes. Transfer to a rack to cool completely.