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Mix together the dry ingredients. With two knives, a pastry blender, your fingertips, or a stand mixer, cut or rub the butter and shortening in until the mixture looks like breadcrumbs.
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Whisk the egg and milk together. Add them to the dry ingredients all at once, mixing quickly and gently for about 20 seconds until you have a soft dough.
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Dump the dough onto a lightly floured work surface. Knead it a couple of times to bring it together. With the help of a dough scraper, shape the dough into a 6" x 6" square, about 3/4" thick. Run a rolling pin over the top once to even it out. Wrap it in plastic wrap, and place it in the freezer for 1 hour.
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Preheat the oven to 400°F.
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Remove the dough from the freezer, unwrap it, and set it on a work surface. It'll be very stiff, but still soft enough to cut with a sharp knife, sharpened dough scraper or rolling cutter (pizza cutter). Cut the dough into nine 2" squares, and place the squares on a lightly greased or parchment-lined baking sheet.
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Bake the biscuits for 16 minutes, or until they're a light, golden brown. Remove them from the oven, and serve hot, warm or at room temperature.
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Store, well-wrapped, on the counter for 3 days. Freeze for up to 3 months.