In a small bowl, combine the warm milk, sugar, and yeast. Stir gently and let sit for 5 to 8 minutes until frothy. In a large bowl (or stand mixer bowl fitted with a dough hook), add the flour and fine sea salt. Pour in the frothy yeast mixture and the egg. Mix on low speed until a shaggy dough forms.

Add the extra virgin olive oil (or softened butter) gradually while mixing. Knead on medium speed for 8 to 10 minutes until smooth and elastic. Form into a ball, place in an oiled bowl, cover, and let rise in a warm spot for 1 to 1.5 hours until doubled in size.

Grease a 9x13-inch baking dish. Punch down the risen dough and turn it out onto a lightly floured surface. Roll into a $12times18$-inch rectangle. Spread the basil pesto evenly, leaving a $frac{1}{2}$-inch border. Evenly sprinkle the shredded mozzarella and grated Parmesan over the pesto.

Roll the dough tightly into a log from the long edge and pinch the seam to seal. Slice into 12 equal rolls using a serrated knife or unflavored dental floss. Arrange cut-side up in the prepared baking dish. Cover and let rise for 30 to 45 minutes until puffy. Preheat oven to $375^circtext{F}$ ($190^circtext{C}$).

Bake for 22 to 27 minutes until the tops are a deep golden-brown and the cheese is bubbling. Let cool for 10 minutes before serving. Brush tops with extra virgin olive oil infused with a little garlic for an extra glossy finish.