In a large bowl, whisk together 2 cups flour, sugar, yeast, rosemary, salt, and ¾ teaspoon pepper.
In a small saucepan, heat milk and butter over medium-low heat until mixture registers 120° to 130° on an instant-read thermometer (butter does not need to melt completely). Add milk mixture to flour mixture, and beat with a mixer at medium speed for 2 minutes. Beat in ½ cup cheese. Gradually beat in enough remaining 2 to 3 cups flour to form a soft dough.
Turn out dough onto a heavily floured surface, and knead until dough is smooth and elastic, 3 to 5 minutes. Spray a large bowl with cooking spray; add dough to bowl, turning to grease top. Cover with plastic wrap, and let rise in a warm, draft-free place (75°) until doubled in size, about 1 hour.
Spray a 10-inch square cast-iron skillet with baking spray with flour. Punch down dough. Turn out dough onto a lightly floured surface; divide dough into 13 portions, and shape each portion into a ball. Place dough balls in prepared pan. Cover and let rise in a warm, draft-free place (75°) until doubled in size, about 35 minutes.
Preheat oven to 375°.
In a small bowl, whisk together egg and 1 tablespoon water; brush onto rolls. Sprinkle with remaining ¼ cup Parmesan and remaining ¼ teaspoon pepper.
Bake until golden brown, 25 to 30 minutes, loosely covering with foil halfway through to prevent excess browning, if needed. Garnish with rosemary, if desired. Let cool on a wire rack for 20 minutes. Serve warm.
Recipe by Southern Cast Iron at https://southerncastiron.com/rosemary-parmesan-black-pepper-rolls/