Place water, milk, egg, 1/3 cup butter, sugar, salt, flour and yeast in the pan of the bread machine in the order recommended by the manufacturer. Select Dough/Knead and First Rise Cycle; press Start.
When cycle finishes, turn dough out onto a lightly floured surface. Divide dough in half. Roll each half into a 12 inch circle, spread 1/4 cup softened butter over entire round. Cut each circle into 8 wedges. Roll wedges starting at wide end; roll gently but tightly. Place point side down on ungreased cookie sheet. Cover with clean kitchen towel and put in a warm place, let rise 1 hour. Meanwhile, preheat oven to 400 degrees F (200 degrees C).
Bake in preheated oven for 10 to 15 minutes, until golden.