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Line a baking sheet with a silicone mat or parchment paper.
Place yeast into bowl of a large stand mixer; whisk 1/2 cup flour and water into yeast until mixture is smooth. Let stand until mixture is foamy, 10 to 15 minutes.
Whisk egg, 3 tablespoons melted butter, sugar, and salt into yeast mixture; add remaining flour and stir.
Fit a dough hook onto stand mixer and knead the dough on low speed until soft and sticky, 5 to 6 minutes. Scrape sides if needed. Poke and prod the dough with a silicone spatula; if large amounts of dough stick to the spatula, add a little more flour.
Transfer dough onto a floured work surface; dough will be sticky and elastic but not stick to your fingers. Form the dough lightly into a smooth, round shape, gently tucking loose ends underneath.
Wipe out stand mixer bowl, drizzle olive oil into the bowl, and turn dough over in the bowl several times to coat surface thinly with oil. Cover bowl with aluminum foil. Let dough rise in a warm place until doubled in size, about 2 hours.
Transfer dough to a floured work surface and form into a 5x10-inch rectangle about 1/2-inch thick. Cut dough into 8 equal lengths. Turn each slice cut-side up and form into a hot dog bun shape about 5 inches long. Transfer dough, cut-sides up, to the prepared baking sheet about set them about 1/4-inch apart.
Cut a slit about 1/8-inch deep down the center of each bun. Brush 2 tablespoons melted butter over the top and sides of each bun. Let rise until almost doubled in size and the buns have risen into each other, about 45 minutes.
Preheat oven to 375 degrees F (190 degrees C).
Bake buns in the preheated oven until golden brown, about 20 minutes. Brush tops with remaining melted butter.