Hot Dog & Hamburger Potato Buns

Directions

1. Preheat the oven to 350º F. Line two baking sheets with parchment paper. In a large bowl, whisk the flour, sugar, and salt together. Add the yeast and mix to combine.
2. Add the water, honey, mashed potatoes, softened butter, and whipped eggs. Mix well with a wooden spoon to combine. Continue mixing (either with the spoon or by gently kneading on a lightly floured surface) until the dough is smooth and well combined, 1 to 2 minutes more.
3. Transfer the dough to a lightly oiled bowl, cover the bowl with plastic wrap, and let rise in a warm place until it doubles in size, 1 to 2 hours.
4. To shape the rolls, turn the dough onto a lightly floured work surface. If you're making both hamburger and hot dog buns, divide the dough in half first, then use one half for hamburger buns, and one half for hot dog buns.
5. To make hamburger buns, divide the dough into 4- to 5-ounce pieces. Fold the dough over onto itself three times, then make a circular cupping motion with your hand, and roll the dough into balls. Don’t use too much flour here, or you won’t get a tight “seal” on your buns.
6. To make hot dog buns, divide the dough into 3- to 4-ounce pieces. Fold the dough over onto itself three times, then roll it like a snake into a long piece of dough (about 3 1/2 to 4 inches long). Use the ends of your hands to taper the ends slightly. Use a bench scraper (or a knife) to gently press into the hot dog buns, forming a line down the center. This will help the rolls split more easily after baking.
7. Transfer the shaped buns to the prepared baking sheets, leaving plenty of room between each (about 1 to 2 inches). Let rise until nearly double in size, about 1 hour.
8. In a small bowl, whisk together the remaining egg, egg yolk, water, and salt. Brush the egg wash evenly on the buns.
9. Bake 10 to 12 minutes, until the buns start to turn golden brown. Remove the pan from the oven, and brush the buns generously with melted butter.
10. Bake 10 to 12 minutes more, or until the buns are deeply golden brown. Brush once again with melted butter and let cool completely.