In a large bowl, dissolve the sugar and then the yeast in the warm water.
Add the milk, oil, salt and 3 cups (360g) of flour to the yeast mixture. Beat vigorously for 2 minutes.
Gradually add flour, ¼ cup (30g) at a time, until the dough begins to pull away from the sides of the bowl.
Turn the dough out onto a floured work surface.
Knead until you have a smooth, elastic dough.
Put the dough into an oiled bowl. Turn once to coat the entire ball of dough with oil.
Cover with a tightly-woven dampened towel and let rise until doubled, about 1 hour.
Turn the dough out onto a lightly oiled work surface. Divide into 18 equal pieces.
Shape each piece into a ball. For hamburger buns, flatten the balls into 3 ½" disks. For hot-dog buns, roll the balls into cylinders, 4 ½" in length.
For soft-sided buns, place them on a well-seasoned baking sheet a half inch apart. For crisper buns, place them 3" apart.
For the second rising, cover with a towel and let rise until almost doubled, about 45 minutes.
Fifteen minutes before you want to bake your buns, preheat your oven to 400°F.
Just before baking, lightly brush the tops of the buns with the egg wash and sprinkle with whatever seeds strike your fancy.
Bake for 20 minutes or until the internal temperature of the bread reaches 190°F when measured with a digital thermometer.
When the buns are done, remove them from the baking sheet to cool on a wire rack.
Split the buns in half and toast or griddle before serving, as desired.
