In the bowl of a stand mixer, fitted with the paddle attachment, combine the flours, yeast, sugar, salt, and starch, and mix until incorporated. On medium-low speed, add the butter, shortening, buttermilk, and egg, and continue to beat until a shaggy dough forms.

Remove the paddle, replace with the dough hook attachment, and on medium-high speed, continue to beat the dough until a smooth mass forms that comes off the sides of the bowl and sticks only a bit to the bottom, about 7 to 9 minutes. If your dough is not sticking at all to the sides or bottom when you begin kneading it with the dough hook, add more buttermilk, a tablespoon at a time, until the dough is wet enough to stick a bit. If it sticks too much, add a bit of flour.

Turn the dough out into a medium bowl that has been greased with oil or sprayed. Turn the dough ball over in the bowl to coat it in oil, cover the bowl with plastic wrap, and set aside to rise for about 1 to 1 1/2 hours, until it has practically doubled in size.

Once the dough has doubled, spray the counter and turn the dough out on to the sprayed surface. Knead the dough once or twice and shape it into an 8" by 12" rectangle. Using a dough scraper, or sharp knife, make 4 cuts down the long side and 4 cuts down the short side of the rectangle, resulting in 16 pieces of dough.

Spray a 13" by 9" by 2" pan with cooking spray and set aside (a pyrex works nicely, as you can see the bottom of the rolls to confirm they are brown before pulling them from the oven). Take each piece of dough and gently form it into a ball, by folding the edges of the dough piece underneath itself, so that the top of the ball is smooth (the bottom will be a bit wrinkly, which is fine).

Place the balls in the prepared pan, making an effort to cover the entire bottom of the pan with the dough. Once all of the balls are in the pan, gently press down on them so they are all touching. Preheat the oven to 375 degrees. Loosely cover the pan with plastic wrap, and set aside for about an hour, until the balls rise to about 1 1/2 times their size.

Once they have risen, brush melted butter on them and place in the oven until the rolls are nicely browned, both on the top and bottom, about 20 to 25 minutes, checking the rolls at about 18 minutes, depending on how hot your oven runs. Remove the rolls from the oven and immediately brush with additional melted butter and sprinkle with Maldon sea salt. Remove the rolls from the pan to cool a bit. When still warm, separate the rolls from each other, slather with butter, and enjoy. Rolls are best fresh, but can be kept in plastic wrap on the counter.