Place water, yeast and 1 tsp of sugar into the bowl attached to a stand mixer with the dough hook attachment fixed on. Stir into combined. Let sit until bubbles appear ( which means that the yeast is proofed.)
Combine the milk, butter, egg, 1/3 cup of sugar, salt and first two cups of the flour. Mix together until the dough comes together.
Add the remaining flour, slowly mixing, until the dough has come together and is slightly tacky to the touch.
Place in a large bowl and cover, Let rise in a warm, draft-free palce until doubled in size, around 45-55 minutes.
Punch the dough down.
Grease (3) 9 inch round pans.
Dived the dough into three equals sections.
Take each section and divide it into 8 pieces. Roll each piece into a ball and place into one pan. Start with a roll in the middle, then place the remaining 7 rolls around it evenly.
Repeat with the other two portions of dough until you have three pans, each pan having 8 rolls in it.
Cover the pans and let rise again until doubled in size, around 40-50 minutes.
Pre-heat your oven to 400 °F.
Bake in preheated oven for 15-20 minutes, until golden brown on top and all of the rolls are cooked. Around 5 minutes before removing from the oven, brush the tops of the buns with the softened butter, then continue to bake until done.