Combine warm water, yeast, and a pinch of sugar in a large bowl. Let sit until foamy, about 5 to 10 minutes.
Add whole wheat flour, 1/4 cup sugar, butter, egg, and salt to the bowl. Mix with a wooden spoon until well combined. If using a stand mixer, stir with the paddle attachment to combine.
Mix in remaining flour about ½ cup at a time until the mixture clears the sides of the bowl. Knead the dough on a floured surface until soft and smooth, adding flour as needed to keep the dough from sticking. If using a mixer, switch to the hook attachment and knead until the dough is smooth and silky.
Place the dough in a lightly greased bowl and turn to coat. Cover and let rise for about an hour.
Divide the dough into 8 evenly-sized pieces. On an un-floured surface, shape the dough into tight rounds and then flatten the balls into 4-inch disks.
Place the buns several inches apart on greased baking sheets. Cover loosely with plastic wrap and let rise for about 30 minutes.
Preheat oven to 375° F.
Whisk egg and 2 tablespoons water to make an egg wash. Brush it lightly over risen buns. Give the tops another brush of the wash before sprinkling generously with seeds.
Bake until golden brown, about 12 to 15 minutes. Remove from the oven and cool on a rack. Slice in half lengthwise to use for burgers or sandwiches.