01 - In a large mixing bowl, combine warm water (about 100°F), sugar, and instant dry yeast. Let the mixture rest for 5 minutes until foamy and active.
02 - Add all-purpose flour, salt, and olive oil to the yeast mixture. Stir until a sticky dough comes together. Turn out onto a lightly floured surface and knead for 7 to 10 minutes until the dough is smooth, elastic, and springs back when pressed.
03 - Place the dough in a greased bowl, cover with a damp towel or plastic wrap, and let rise in a warm spot for 1 hour or until doubled in size.
04 - Preheat the oven to 375°F. Line a baking sheet with parchment paper and set aside.
05 - Punch down the risen dough and roll it out on a floured surface into a 12 by 16-inch rectangle. Spread basil pesto evenly across the surface, leaving a small border around the edges. Sprinkle shredded mozzarella and grated parmesan uniformly over the pesto layer.
06 - Starting from one long edge, roll the dough tightly into a log. Using a sharp knife, slice the log in half lengthwise to expose the layers. With the cut sides facing up, intertwine the two halves together, gently pressing the ends to seal.
07 - Carefully transfer the braided loaf to the prepared baking sheet. Brush the surface evenly with beaten egg for a golden finish.
08 - Bake for 28 to 32 minutes until the crust is deep golden and the cheese is bubbling through the braids.
09 - Remove from the oven and immediately brush with melted butter. Optionally sprinkle with additional parmesan and chopped fresh basil. Allow to cool for 10 minutes before slicing into portions.