In the bowl of a stand mixer fitted with the dough hook, combine the flour with the yeast, sugar and salt. Add the milk, egg and the 4 tablespoons of softened butter and mix at medium speed until the flour is fully incorporated, 3 to 4 minutes. If your dough seems sticky, then gradually add more flour, one tablespoon at a time. Cover the bowl with plastic wrap and let sit at room temperature (we like a warm place like our stove top) until almost doubled in size, about 1 hour.

Brush a 9-by-9-inch metal baking pan with 1 tablespoon of the melted butter.

Lightly flour a work surface and then turn out the dough. Punch the dough down, then divide into two equal portions. Roll each half into a 12-inch square, about ¼-inch thick. Brush each square of dough with 2 tablespoons of the melted butter. Sprinkle each half with ⅓ cup of parmesan cheese and then top with a generous amount of cracked pepper. Cut each square into six 2-inch-wide strips.

Roll each strip into a coil and then arrange seam side down in the prepared baking pan. Cover with plastic wrap and let rise at room temperature for 30 minutes.

Preheat the oven to 350°F. Bake the rolls until puffed and golden brown, 20 to 25 minutes. Remove from the oven and brush with the remaining 1 tablespoon of melted butter. Finish with more cracked black pepper, parmesan cheese, and sprinkle with flaky sea salt and fresh thyme, if using. Serve warm.