I like to sneak a bit of light brown sugar into almost everything I make. I love the flavor of the molasses in brown sugar. White sugar, a peerless product in many ways, doesn't taste like anything but sweet. Using brown sugar, like toasting nuts before adding them to a recipe, adds another level of flavor. You won't think "Oh, this tastes like brown sugar." You'll simply think "Oh, this is the best shortbread I have ever had."
Homemade shortbread with ice cream is one of the coziest desserts you could possibly make for a dinner party of friends. Though it used to be commonplace (under the name short'nin' bread), almost no one bakes it at home any more. It's a snap.
Preheat the oven to 350 degrees F. Line a 10 by 14 1/2-inch sheet pan (with sides) with parchment or waxed paper.
In a mixer fitted with a paddle attachment (or using a hand mixer), cream the butter until soft and smooth. Add the brown sugar and mix until incorporated.
In a separate bowl, stir together the flour and cornstarch. Add to the butter mixture and mix at low speed just until the ingredients are incorporated and the dough comes together. Turn the dough out onto a floured work surface and knead it 5 to 10 times, just to smooth the dough.
Reflour your work surface. With a rolling pin, roll the dough out to fit the sheet pan. To transfer to the sheet pan, roll the dough up onto the rolling pin, lift it up, and unroll into the pan. Using light strokes of the rolling pin, roll the dough evenly into the corners and edges of the pan, and roll out any bumps. (Or, press the rolled-out dough thoroughly into the pan with your fingers.) Prick the shortbread all over with a fork to prevent any buckling or shrinking.
Bake in the center of the oven for 15 minutes. After 15 minutes, rotate the pan and knock it once against the oven rack, to ensure even cooking and a flat surface. Bake 10 to 15 minutes more, until very lightly browned.
Immediately sprinkle the granulated sugar evenly over the surface. Let cool 10 minutes, then cut into 1 1/2 by 3-inch bars. Let cool completely in the pan, then store in an airtight container.
Recipe courtesy of Gale Gand, "Butter Sugar Flour Eggs" by Gale Gand, Rick Tramonto, Julia Moskin, Clarkson N. Potter Publishers, 1999