Serve with veggie burgers and all your favorite fixings. Makes 8 (3 1/2-inch) burger buns. If you like, make slider buns by cutting the dough with a smaller 2 ¼-inch cutter.
In the workbowl of a heavy-duty mixer, or in a large bowl, mix the yeast with 3 cups of the whole wheat flour.
In another bowl, whisk together the hot water, honey, oil, and salt. Add the egg.
With a wooden spoon, mix the liquid ingredients into the flour and yeast. If using a stand mixer, fit it with the dough hook and knead at low speed. Otherwise, turn the dough out onto a lightly floured surface and knead by hand. Knead 4 or 5 minutes, adding the remaining 1/2 cup of flour a tablespoon at a time, as needed, until the dough is smooth and elastic.
Place in an oiled bowl at least twice the volume of the dough. Cover with plastic wrap and let rise in the refrigerator until the dough has doubled, about one hour.
Gently turn the chilled dough onto a lightly floured surface and press into a rounded rectangle with your hands. Use a rolling pin to roll to a thickness of ½ inch (not thinner.)
Cut 8 circles out of the dough with a 3- or 3 ½-inch round cutter. (see note)
Brush a baking sheet with oil or spray with cooking spray. Arrange the buns on the pan, allowing room for sideways expansion. Cover very loosely with plastic wrap and let rise at room temperature about 45 minutes. Preheat oven to 400°F.
Make an egg wash with the egg and a teaspoon of water. (You will have egg wash left over—use it for French toast!)
When the buns have risen, brush them lightly with egg wash and sprinkle with sesame seeds.
Bake 10 to 12 minutes until the buns are lightly golden. Cool before slicing in half.
Notes
Make slider buns: cut the dough with a 2 ¼-inch cutter.