In your stand mixer, combine all-purpose flour and instant yeast. Gradually pour in whole milk along with one egg, neutral oil, kosher salt, and granulated sugar. Using a dough hook, mix on low speed for about 30 minutes until the dough becomes smooth and elastic, pulling away from the sides of the bowl.

While the dough rises, grab your food processor. Add garlic and toasted pine nuts and blend until finely chopped. Gradually add the fresh basil and olive oil, processing until you achieve a smooth consistency. Stir in freshly grated Parmesan cheese.

Transfer the dough onto a lightly floured surface, folding gently to release any air bubbles. Allow the dough to rest for 20 minutes, covering it with a kitchen towel.

After resting, roll the dough into a 16"x10" rectangle on your floured surface. Carefully spread the pesto evenly over the surface.

Starting from the top edge of the rectangle, tightly roll the dough down to create a log shape. Cut the log in half lengthwise and twist each half together to form a braid.

Place the braided bread in a parchment-lined loaf pan and cover with a kitchen towel. Allow it to rise for 2 to 2.5 hours until the dough has doubled in size.

Preheat your oven to 375°F (190°C). Brush the top of the braided bread with an egg wash and bake for 45 to 50 minutes, or until golden brown and sounds hollow when tapped.