In the bowl of a stand mixer, combine 1 1/2 cups flour with yeast.
Combine milk, butter, sugar, and salt, and heat (in microwave or stovetop) to 120 degrees.
Add warm liquids to flour and yeast mixture and mix for 2 minutes with dough hook attachment.
Add egg and mix to combine. Add enough additional flour to form a soft dough.
Turn dough out onto floured surface and knead for 3-4 minutes. Place dough back in mixing bowl, and cover with a tea towel. Let rise in a warm place for 1 hour, or until doubled in size.
Turn dough out on to floured surface, and divide into 12 pieces. Shape each piece into a ball and then flatten slightly. Place on a greased baking sheet. Cover with plastic wrap or towel to let rise for 45-60 minutes, until doubled in size.
Preheat oven to 350 degrees. Bake buns for about 15 minutes, or until lightly browned. Watch carefully to prevent over browning.
Remove from baking sheet and cool on a wire rack.
Extra buns can be frozen for later use.