Pesto and Parmesan Rolls

In a small bowl, combine warm water, warm milk, sugar, and yeast. Let it sit for 5-10 minutes, until the mixture becomes frothy.
In a large bowl, mix together the flour and salt. Make a well in the center and pour in the yeast mixture, olive oil, and egg. Stir until the dough begins to form.
Knead the dough on a lightly floured surface for about 5-7 minutes, or until smooth and elastic.
Place the dough in a greased bowl, cover with a clean towel, and let it rise in a warm place for 1 hour, or until doubled in size.
Prepare the Filling:

In a small bowl, mix the pesto with melted butter and Parmesan cheese until smooth and well combined.
Shape the Rolls:

Once the dough has risen, punch it down and turn it out onto a floured surface. Roll it into a rectangle (about 12×8 inches).
Spread the pesto mixture evenly over the dough, leaving a small border along the edges.
Starting from one long edge, roll the dough tightly into a log. Cut the log into 10-12 even slices.
Assemble and Bake:

Arrange the rolls in a greased or parchment-lined 9×13-inch baking dish. Cover with a towel and let them rise for an additional 20-30 minutes, until puffed up.
Preheat your oven to 375°F (190°C).
Sprinkle the grated Parmesan over the rolls and bake for 20-25 minutes, or until golden brown and the cheese is bubbly.
Serve:

Once baked, remove the rolls from the oven and let them cool for a few minutes. Garnish with chopped fresh basil, if desired, before serving.
Serving and Storage Tips: