Heat the milk in a small saucepan over medium heat just until it comes to a boil. Remove from heat and let stand until cooled to warm room temperature.

Sprinkle yeast over water in bowl of a stand mixer (or large mixing bowl.) Add 1/2 tablespoon sugar and let stand until foamy, about 5 minutes.

Beat in the remaining tablespoon sugar, egg and 2 tablespoons melted butter. Beat in cooled milk. Gradually add the flour and salt, scraping down side of bowl, until a soft, sticky dough forms. Knead dough for 10 minutes, adding up to an additional 1/2 cup flour if dough is unmanageably sticky.

Grease a large bowl. Place the dough in the bowl. Cover with plastic wrap and place in a warm, draft free location until doubled in size, about 1 1/2 hours.

In a small bowl, stir together all of the ingredients for the filling. Line with parchment paper and coat a 9-inch round cast iron skillet or baking pan with butter or nonstick baking spray.

Punch down the dough and transfer to a lightly floured work surface. Roll dough to 12x8-inch rectangle.

Spread the cheddar mixture over the dough, leaving a 1-inch border on the sides. Roll the dough length-wise to a 12-inch log, pinch the seam to seal.

Cut crosswise into 8 thick slices and arrange in prepared skillet or baking pan. Brush the rolls with the remaining melted butter. Cover with plastic wrap and let rise a second time in a warm, draft free location until buns are puffed and almost doubled in size, about 30 to 45 minutes.

Heat oven to 350°F and bake buns until they are golden-brown and bubbly, 35 to 45 minutes. Transfer to a wire rack and let cool 10 minutes. Enjoy warm.