Combine 3/4 cup warm water, the yeast, and 1 teaspoon of the sugar in a small bowl; proof for 5 minutes until foamy.
In the bowl of a stand mixer fitted with a dough hook, add the all-purpose and whole wheat flours with the sea salt and mix briefly to combine. Add the remaining sugar, room temperature butter or extra-virgin olive oil, the large egg, and the yeast mixture; mix on medium-low speed for 5 to 7 minutes until the dough is smooth and forms around the hook, stiff but not sticky.
Turn the dough out onto a clean work surface, knead briefly to form a ball, and place in a large bowl. If the dough is sticky, add a bit of flour to the work surface. Cover with plastic wrap and set aside in a warm spot for 1 hour, until nearly doubled.
Line a large baking sheet with parchment paper. Turn the dough out onto a clean, unfloured work surface and divide into 8 pieces. Shape each piece into a ball by rolling it on the countertop with a cupped hand, place on the baking sheet, and flatten each into a 3-inch disk. Cover with plastic wrap and let rise for 1 hour; they will puff slightly but remain somewhat flat.
Preheat the oven to 375°F.
In a small bowl, whisk together the egg white and 1 tablespoon water to make the egg wash.
Bake the uncovered buns and at the 13-minute mark brush the tops with the egg wash and sprinkle with sesame seeds, then continue baking until the buns are puffy and the tops are lightly golden, total bake time about 15 to 18 minutes.
Let the baked buns cool on a wire rack.