In a large bowl, combine the warm water, sugar, and yeast. Let it sit for 5-10 minutes until foamy and bubbly.
Add the olive oil, beaten egg, salt, and 2 cups of flour to the yeast mixture. Mix with a dough hook or by hand until combined into a shaggy dough.
Gradually add the remaining 1 cup of flour, mixing until a soft, slightly sticky dough forms.
Knead the dough for 6-8 minutes on a lightly floured surface until it becomes smooth, elastic, and springs back when poked.
Place the dough in a lightly oiled bowl, cover it with a damp cloth, and let it rise in a warm place for 1 to 1.5 hours, or until doubled in size.
While the dough is rising, mix together the melted butter, minced garlic, chopped parsley, and Italian seasoning in a small bowl.
Once the dough has risen, punch it down and turn it out onto a lightly floured surface. Roll the dough out into a 9×12 inch rectangle.
Brush the entire surface with the garlic herb butter mixture, leaving a small border around the edges. Sprinkle the mozzarella and Parmesan cheese evenly over the buttered dough.
Starting from one of the long sides, tightly roll the dough into a log. Pinch the seam to seal it and place the log, seam-side down, in a greased 9×5 inch loaf pan.
Cover the loaf pan and let the dough rise for another 30-45 minutes, or until it has risen about an inch above the pan.
Preheat your oven to 375°F (190°C).
Bake the bread for 25-30 minutes, or until the top is golden brown and the loaf sounds hollow when tapped.
Let the bread cool in the pan for 10 minutes before transferring it to a wire rack to cool for at least 15 more minutes before slicing.
Notes
Ensure your yeast is not expired and water temperature is between 110-115°F for proper rising. The foamy step after adding warm water confirms yeast is active.
Grate cheese from blocks for better melting and flavor compared to pre-shredded varieties.
If top browns too quickly, tent loosely with foil for the last 10 minutes of baking.
Grease the loaf pan with butter, oil, or cooking spray before adding the dough.