Mix together the milk, water and yeast in a large bowl. Allow to rest for 5 minutes until it becomes bubbly. Measure flour by spooning and lightly leveling the top with a knife. Sprinkle flour over yeast mixture. Add egg, olive oil and salt to the bowl. Mix until a shaggy dough starts to form then knead for 6-8 minutes, until smooth. Place in an oiled bowl, cover, and let rise for 45 minutes to 1 hour, until doubled.
Assembly
Divide the dough into four pieces and shape into balls. Cover and let rest for 10 minutes. Place one piece of dough on a piece of parchment. Roll it into a 10-inch circle. Brush the circle all over with egg wash. Evenly spread ⅓ cup of pesto and top with ⅓ cup of cheese. Layer with another 10-inch circle and repeat with pesto and cheese. Continue to repeat until you have 3 layers of filling and 4 layers of dough.
Shaping
Place a 2-inch round biscuit cutter or drinking glass in the center of the dough making a small indentation to act as a guide. Cut around the circle using a bench scraper creating 16 equal sized strips. Take two strips next to each other, twist them away from one another and pinch the ends so they stick. Repeat. Let rise for 45 minutes or until puffy.
Bake
To bake: Slide parchment paper onto a baking sheet and lightly brush with eggwash. Bake in a 400°F preheated oven for 20-23 minutes or until golden and cooked throughout. Remove from oven and allow to cool for at least 10 minutes before serving.