To make shortcake: Preheat oven to 425 degrees and place rack in middle position. Line a baking sheet with parchment paper.
In a large bowl, whisk together flour, 2 tablespoons granulated sugar, brown sugar, baking powder and salt.
Add cold butter pieces, working them into the flour with a pastry cutter, or your fingers, until the mixture resembles cornmeal and no large lumps of butter remain.
In a small bowl, whisk together half-and-half and egg. Stir into flour mixture until dough comes together in a sticky mass.
Turn dough out onto a lightly floured counter and knead lightly until it comes together, about 30 seconds. Dust the counter with a bit more flour, then pat dough into a rectangle about 1/2-inch thick. Cut 6 rounds with a floured 3-inch biscuit cutter, pressing straight down — twisting can seal the layers, leading to a dense shortcake — then place them upside-down on a baking sheet (helps ensure the highest rise).
No biscuit cutter? You also can cut squares with a knife.