Grease a 9x13-inch baking dish, and set aside.
In the bowl of a stand mixer on low speed, use a dough hook to combine 3 cups (360 g) of flour, milk, yeast, salt, melted butter, and egg.
1 ½ cups milk, 2 tablespoons instant yeast, 1 teaspoon salt, 4 tablespoons unsalted butter, 1 large egg
Add additional flour ¼ to ½ cup (30 g - 60 g) at a time until the dough begins to pull away from the sides of the bowl. Adjust the speed to medium for 5-6 minutes. The dough should be smooth, elastic, and not sticky.
Form the dough into a smooth ball, and transfer it to a large, lightly greased bowl. Cover it with a clean kitchen towel, and allow it to double in size, about 30 minutes to an hour depending on the room temperature.
After the dough has doubled in size, punch it down to deflate it. Separate the dough into about 12 equal different pieces. We like to weigh the dough to ensure the pieces are the same size.
Roll the pieces into balls, and place them into the prepared 9x3-inch baking dish. Cover with a clean towel or piece of greased plastic wrap, and allow to double in size, about 30 minutes to an hour.
While the rolls rise, preheat the oven to 350°F.
Bake the rolls for 17-22 minutes or until the tops are golden brown. Brush the tops with melted butter, and serve warm.
See post below for storage options, tips, and answers to frequently asked questions.