Add the ingredients to the bread machine. Place all dough ingredients (flour, water, salt, sugar, butter, egg, and yeast) into the bread machine, following the order recommended by your machine’s manufacturer. Then, select the dough cycle and press start.
Monitor the dough consistency. During the first few minutes of mixing, check the dough’s consistency. It should be smooth and slightly tacky, pulling away cleanly from the sides of the bread machine bucket. If the dough is too sticky, add 1 tablespoon of flour at a time. If it’s too dry, add 1 teaspoon of water at a time. Let the cycle complete.
First rise. When the machine beeps, the dough should be soft, puffy, and have risen significantly. It should almost reach the top of the bread machine bucket.
Divide and shape. Turn the dough out onto a lightly floured surface. Using a sharp knife or dough scraper, divide the dough into 8 equal pieces. (For even rolls, divide the dough in half, then in quarters, and so on.) Then, gently shape each piece into a round ball by pulling the sides of the dough underneath to create a smooth top. Place the shaped rolls onto a parchment-lined baking sheet, leaving about 2 inches of space between each roll. Gently flatten them with your palm to form a slight dome. Brush each roll with the beaten egg and sprinkle with sesame or poppy seeds. Second rise. Cover the rolls loosely with heavily greased plastic wrap to prevent sticking. Then, place the baking sheet in a warm spot and let the rolls rise until they are very puffy, about 45 minutes. Toward the end of the rising time, preheat your oven to 375°F (190°C), with the rack positioned in the center.
Bake. Bake the rolls for 14-17 minutes until they are golden brown. The egg wash will give them a shiny, richly colored crust. The rolls should feel firm outside but soft to the touch.
Let it cool. Remove the rolls from the oven and transfer them to a wire rack to cool completely. For best results, wait until the buns are fully cooled before slicing.