In a large bowl for a stand mixer, add milk, water and yeast. Stir lightly and let stand for 5 minutes until bubbly.
Add egg, salt, olive oil and 1 cup of flour. Mix.
Add remaining flour one cup at a time, mixing between each addition.
Knead dough in machine for 5 minutes or by hand for 10 minutes.
Place in a large bowl that has been lightly greased with olive oil. Cover and let rise until doubled, about 1 hour.
Gently deflate dough and divide into two.
Roll out first piece into a long rectangle, approximately 6 X 18"
Filling
Add ¼ cup of the pesto and half the parmesan cheese.
Roll dough together to form a long log. Place seam side down on a baking sheet lined with parchment paper or directly on the baking sheet lightly greased with olive oil.
Form bread into an "S" tucking ends into the log.
Gently slice through the top of the bread with a sharp knife. You want to slice through about a ¼ of an inch.
Repeat with second piece of dough.
Cover and let rise for about 30 minutes.
Topping
Just before baking, brush olive oil on the dough and sprinkle on parmesan cheese.
Bake in a preheated 350 degree oven for 30 minutes.
Allow bread to cool on a baking rack before slicing.