Cut 4 tablespoons of the unsalted butter into small cubes and add it to 1 cup whole milk in a microwave-safe measuring cup. Heat until the mixture reaches 120°F to 130°F. The butter does not need to melt completely.

Pour the warm milk mixture into the flour mixture and add 1 large room-temperature egg. Mix with the dough hook on low speed for about 1 minute, scraping down the bowl if necessary, until a shaggy dough forms.

Increase the mixer to medium-low speed and knead for 5 to 6 minutes. The finished dough should become smooth and elastic but remain soft and slightly tacky. It may still cling slightly to the bottom of the mixer bowl. If the dough is genuinely wet and difficult to handle after kneading, add additional all-purpose flour 1 tablespoon at a time, using no more than 2 tablespoons unless absolutely necessary.

Cover the dough and let it rest for 10 minutes.

Soften 1 tablespoon of the unsalted butter, then use it to grease the bottom and sides of a 9x13-inch baking dish.

Divide the dough into 12 equal pieces. Pull the edges of each piece underneath and gently roll against the work surface with a cupped hand until the top is smooth and round.

Arrange the 12 dough balls evenly in the prepared 9x13-inch baking dish in 3 rows of 4. Cover loosely with plastic wrap or a clean kitchen towel and let rise in a warm, draft-free place for 30 to 60 minutes, or until the rolls are very puffy and touching or nearly touching one another.

During the final 20 minutes of rising, preheat the oven to 350°F.

Bake the rolls at 350°F for 20 to 25 minutes, or until evenly golden brown. An instant-read thermometer inserted into the center of a middle roll should register 190°F to 195°F.

Melt your remaining 2 tablespoons unsalted butter. Remove the rolls from the oven and immediately brush the melted butter evenly over the tops. Let the rolls cool in the baking dish for about 10 minutes, then serve warm. ENJOY!