01 - In a large mixing bowl, combine the warm water, sugar, and yeast. Stir gently and let rest for 5 minutes until the mixture becomes foamy and fragrant.
02 - Add the flour, salt, and olive oil to the yeast mixture. Stir until a sticky dough begins to form. Turn out onto a floured surface and knead for 7–10 minutes until the dough is smooth, elastic, and springs back when pressed.
03 - Place the dough in a lightly 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 12×16-inch rectangle. Spread the basil pesto evenly across the surface, leaving a small border around the edges. Sprinkle the mozzarella and Parmesan cheeses in an even layer over the pesto.
06 - Starting from the long edge, roll the dough up tightly into a log. Using a sharp knife, cut the log in half lengthwise. With the cut sides facing up, twist the two halves around each other to form a braid, pinching the ends together to seal.
07 - Carefully transfer the braided loaf to the prepared baking sheet. Brush the surface generously with the beaten egg for a golden, glossy finish.
08 - Bake for 28–32 minutes until the crust is deep golden brown and the cheese is bubbling and melted throughout.
09 - Remove from the oven and immediately brush with melted butter. Sprinkle with additional Parmesan and chopped fresh basil if desired. Allow to cool for 10 minutes before slicing into portions.