Dissolve sugar in warm water in a medium bowl; stir in yeast until bubbly. Stir in butter, 1 tablespoon rosemary, salt, and Italian seasoning. Stir in 2 cups flour; gradually add remaining 1 cup flour to form a workable dough.

Transfer dough to a lightly floured surface; knead 10 to 12 minutes.

Coat the inside of a large bowl with olive oil. Place dough in the bowl and turn to coat. Cover bowl; let rise in a warm place until doubled in volume, about 1 hour.

Punch down dough; divide in half. Line a baking sheet with parchment paper; lightly grease parchment paper. Shape dough into 2 round loaves; place on the prepared baking sheet. Sprinkle with remaining 1 tablespoon rosemary. Cover loaves; let rise until doubled in volume, about 1 hour.

Preheat the oven to 375 degrees F (190 degrees C).

Brush loaves with beaten egg. Bake in the preheated oven until golden brown, 15 to 20 minutes.