In a mixing bowl, combine lukewarm water with a pinch of sugar. Sprinkle the yeast over the water, stir gently, and let it rest for 5 minutes until the mixture becomes frothy.
Microwave the milk and butter for 1 minute or until the butter has melted. Once the yeast mixture has proofed, combine with the warmed milk and butter mixture.
Gradually add flour and the salt into the yeast and milk mixture and knead with a mixer or by hand. Continue adding flour gradually until the dough starts to pull away from the sides of the bowl.
Knead for 5 minutes, until the dough becomes smooth and elastic.
Cover the bowl with a clean kitchen towel and let the dough rise in a warm, draft-free spot for approximately 20 minutes.
After the dough has risen, gently flatted it and roll it up to form the desired loaf shape. Pinch the ends to seal and place the loaf on a parchment-lined baking sheet or in a greased loaf pan.
Cover the loaf with a clean towel and let it rise for another 30 minutes. While the dough rises, preheat your oven to 425°F.
Then, score the top of the loaves with a sharp knife or scoring blade, and brush over the egg wash (egg + water).
Bake the loaves for 16 minutes, or until it turns a rich golden brown. Sprinkle with parmesan and rosemary, and bake for an additional 2 minutes, until the cheese has melted.
Let the bread cool before cutting and serving.