In the bowl of a stand mixer fitted with a dough hook (or in a large bowl if planning to mix by hand), combine 2 cups of the bread flour, the yeast, sugar and salt. Add the warm water mixture, followed by the beaten eggs, mixing on low speed until incorporated.

Add the remaining bread flour 2 tablespoons at a time while mixing on medium low speed until dough almost clears the bowl and is only a slightly sticky to the touch (It's okay if some dough sticks to your fingers). You may not need all of the remaining flour, or you may need more than is called for. Knead until smooth and elastic, about 5-7 minutes more.

Gather dough into a ball and place in a greased bowl. Cover with plastic wrap and put in a warm place and allow to rise until doubled, 1 to 2 hours.

Punch down dough and let rest for a few minutes. Divide dough into eight equal pieces and shape into balls. Place on a sheet pan lined with parchment paper. Spray some plastic wrap with non-stick cooking spray and place over the shaped buns. Return to a warm place and continue to rise for an additional 30 minutes to 1 hour.

Bake until golden brown, about 10 minutes. Cool completely on a wire rack.