In a large bowl, weigh bread flour, sugar, salt, and yeast. Whisk to combine. Using a stand mixer with the beater blade or a handheld mixer, turn on low and slowly pour in the milk and butter. Increase speed to medium and beat for 5 minutes.
Cover the bowl with plastic wrap and place in a warm, draft-free area until doubled in volume, about 2 hours. You can use it immediately after rising, or refrigerate the dough for up to 7 days.
Pour about 2-3 tbsp of the olive oil into the bottom of a 12-inch cast iron skillet* (See notes below)
Dump half the dough** on top of the olive oil and add about 2-3 tbsp more on top of the dough. Using your fingertips, dimple the dough and gently spread it to the sides of the skillet/pan. Cover and let rise until a little larger in size, about ½ an hour. (It won't be doubled in size).
Preheat oven to 400 degrees. When dough has risen, sprinkle the rosemary, sea salt, cracked pepper, and Parmigiano Reggiano over the top and bake for about 25-30 minutes, or until golden brown.
Serve warm with pasta or use as a sandwich bread by slicing pieces in half horizontally.