Gather the ingredients.

Combine 1 (¼-ounce) package (2 ¼ teaspoons) active dry yeast or bread machine yeast and ½ cup warm water (about 110 F) in a large bowl or bowl of a stand mixer. Let the mixture stand for about 10 minutes, until foamy.

In a small bowl, whisk ⅔ cup whole milk (room temperature) , 1 large egg , and 3 tablespoons unsalted butter (melted and cooled) together to blend.

Add the milk mixture to the yeast mixture along with 2 ½ tablespoons sugar , 1 ¼ teaspoons salt , and 3 cups all-purpose flour .

Knead the dough by hand (or using a stand mixer with the dough hook) for 8 to 10 minutes, adding a little more flour if necessary to keep the dough from sticking to your hands, the countertop, or the sides of the bowl. The dough should be smooth and elastic at this point.

Generously grease a large bowl with butter or oil . Gather the dough into a ball and place it into the greased bowl. Turn it over a few times to coat the dough thoroughly.

Cover the bowl with plastic wrap and let the dough rise for 1 to 1 ½ hours, or until it has doubled in bulk.

Line 2 large baking sheets with parchment paper or lightly grease the pans.

Punch down and pat the dough into a rectangle.

Cut the dough into 18 pieces, about 1 ½ to 1 ¾ ounces each (or smaller).

Shape the dough pieces into firm balls, flatten them slightly with your hand, and place them on the prepared baking sheets 2 to 3 inches apart.

Cover the buns with a lightweight kitchen towel and let them rise in a draft-free spot for about 30 minutes.

Preheat the oven to 375 F and arrange racks in the lower and upper thirds of the oven. If using the egg wash, whisk the egg white with 1 tablespoon of water until blended.

Before placing in the oven, brush each roll with the egg wash and sprinkle with sesame seeds or poppy seeds if using.

Bake for 15 to 18 minutes, or until golden brown.

If you didn't use the egg wash and seeds, brush with melted butter if desired. Let the buns cool on a rack.

Split the buns apart and stuff them with sandwich fillings.

Gather the ingredients.

In a small bowl, whisk together ½ cup water (warm) , ⅔ cup whole milk (room temperature) , 1 large egg , and 3 tablespoons melted butter (slightly cooled) .

Place the milk mixture along with the 3 cups all-purpose flour , 2 ½ tablespoons sugar , 1 ¼ teaspoons salt , and 1 (¼-ounce) package active dry yeast or bread machine yeast in the bread machine in the order suggested by the manufacturer.

Set to the dough cycle.

Remove the finished dough to a lightly floured surface. Flatten into a rectangle, cut into pieces, and shape the dough into balls. Place on 2 parchment-lined baking sheets, cover with a kitchen towel, and let rise for 30 minutes.

Brush with the egg wash and seeds , if using, and bake in a 375 F oven for 15 to 18 minutes.

If desired, brush with melted butter if the egg wash and seeds weren't used . Let the buns cool on a rack.

Split the buns in half, add sandwich fillings, and enjoy.