In a large bowl, whisk together warm milk, sugar, and yeast. Let sit 5–10 minutes until bubbly and foamy.
Add flour, salt, and olive oil to the yeast mixture. Stir until a shaggy dough forms. Turn out and knead on a floured surface for 8–10 minutes until smooth and elastic. (Or knead in a stand mixer with the dough hook for 6 minutes.)
Transfer dough to a greased bowl. Cover with a towel or wrap and let rise in a warm spot for 1 hour or until doubled in size.
In a bowl, stir together the melted butter, garlic, parsley, salt, pepper, mozzarella, and parmesan until combined.
Roll out dough into a large rectangle, about ¼-inch thick. Spread the entire garlic butter mixture evenly across the surface.
Using a sharp knife or bench scraper, cut the dough into 3-inch wide strips, then stack them on top of each other. Cut the stack into even pieces (roughly the height of your loaf pan).
Turn the stacked pieces sideways and place them into a greased 9x5” loaf pan, cut sides facing up like a deck of cards. Loosely cover and let rise 25–30 minutes.
Preheat oven to 350°F (175°C). Bake loaf for 30–35 minutes, until golden and the center is set.
Let cool in pan 10 minutes, then gently lift out to a wire rack. Pull apart and enjoy warm.