In large bowl, 2 cups all purpose flour, whole wheat flour, salt, sugar and yeast and form a well in the center.
In small bowl, whisk egg with oil and warm water (110-115º F or 43-46°C).
Pour liquid into flour and stir together as much as possible. Not all flour will be incorporated.
Transfer dough and bits onto a lightly floured surface and knead for 6 to 8 minutes to form a smooth, elastic dough. Add as much of the remainder of the all purpose flour as needed to prevent sticking (no need to use it all). Dough is ready when it holds it shape, springs back when poked and feels smooth. It is difficult to over-knead dough by hand, so knead away!
Shape dough into a ball and place in a lightly oiled bowl, turn dough to coat evenly with oil. Cover with a clean towel and let rest for 1-2 hours until dough has doubled.
Punch down dough to release air.
Split dough into 12 equal pieces, about 3 1/4 to 3 1/2 ounces (92 to 99 grams) each. The more uniform the better - a kitchen scale is very helpful.
Shape each piece into a hamburger bun shape - a slightly flattened ball. Shape top by holding dough in hand then stretching dough by pulling and pinching extra dough towards the bottom. Place dough on counter, cup the ball with your palm and gently squeeze and rotate with cupped hand to smooth bottom and shape dough. (See video in post).
Place on a greased baking sheet, sprinkle with cornmeal if desired. Gently press top of balls to flatten if too round.
For a soft, shiny crust with seeds (sesame, chia, poppy, hemp, etc.), mix egg and water. Gently and lightly brush onto buns. Sprinkle with seeds.
Cover dough with cloth and let rise until double, 45-60 minutes.
Bake in a preheated 375°F (190°C) oven for 15 to 20 minutes until dark golden brown.
Remove from pan and cool on wire rack.
Notes
White Buns - For extra soft, fluffy buns, omit the whole wheat flour and use just all purpose flour.Flax Buns - For extra fiber and Omega3, add 3 Tbsp ground flax when using just all purpose flour. If using whole wheat flour, you may need to add more liquid (I have not tested this recipe with whole wheat flour and ground flax).Cool completely before storing in sealed bag for up to 3 days at room temperature.Freeze baked buns for longer storage.