Pour the culture into a mixing bowl.  Add the water, milk, salt, sugar, half of the butter, and the beaten egg and mix.  Add the flour a cup (140 g) at a time until the dough is too stiff to mix by hand.  Turn out onto a floured board and knead in the remaining flour until the dough is smooth and satiny.

Proof the dough overnight (8 to 12 hours) at room temperature, about 70°F (21°C), in a large bowl covered with plastic wrap.  During this time, the dough should double in size.  After the proof, use a spatula to gently ease the dough out onto a floured board.  Allow the dough to rest for 30 minutes.  If marked flattening occurs during this time, knead in additional flour before shaping.

Roll the rested dough into a rectangle about 5 inches (12 cm) wide and 1/2 inch (1.5 cm) thick.  Brush the remaining half of the butter over the dough.  Cut into 4 strips lengthwise with a pizza cutter.  Stack the strips with the buttered sides up.  Cut the stacked strips into eight to ten 1 1/2-inch (4 cm) pieces.  Put the rolls in the cups of a muffin pan with the cut sides facing down so that the layers are visible on top.

Proof for 2 to 4 hours, until doubled in bulk.  Proof for the first hour at room temperature and then at 85° to 90°F (29° to 32°C) in a proofing box.

Bake in a preheated oven at 400° (200°C) for 12 to 15 minutes, or until brown.  Remove the rolls from the pan and let cool on a wire rack.

Happy Baking!!!  And enjoy the fall weather.