Step 1

Place flour, sugar, yeast, and salt in bowl of a stand mixer fitted with a paddle attachment. With mixer running on low speed, beat in warm milk and butter. Beat on low speed until just combined, 30 to 45 seconds. Remove paddle attachment from mixer; attach dough hook. Beat on medium speed until dough is smooth and elastic, about 6 minutes. Transfer dough to a medium bowl coated with cooking spray. Cover with plastic wrap and let rise in a warm spot until doubled in size, about 1 hour, 30 minutes.

Step 2

Stir together butter, Parmesan, parsley, rosemary, garlic, salt, and pepper in a small bowl until well combined. Set aside.

Step 3

Punch dough down in bowl and transfer to a lightly floured work surface. Divide dough evenly into 12 pieces (about 1 1/2-ounce; 3 tablespoons each). Flatten each piece into a 4-inch-round disk (doesn't need to be perfectly round). Spread about 1 tablespoon filling onto 1 side of each disk. Stack disks, cheese side up, on top of each other. Turn stack of dough onto its side, and place in an 8 1/2- x 4 1/2-inch loaf pan coated with cooking spray. Slightly separate disks in loaf pan. Cover with plastic wrap and let rise until almost doubled in size, about 45 minutes. Preheat oven to 325°F.

Step 4

Bake loaf in preheated oven until golden brown, 45 to 50 minutes, covering loosely with aluminum foil if needed to prevent overbrowning. Transfer loaf pan to a wire rack, and let cool 10 minutes. Invert loaf onto wire rack, turn upright, and let cool about 20 minutes. Brush with melted butter, and sprinkle with sea salt.