In a measuring cup or small bowl, whisk together the milk and egg.
In a food processor, combine the flour, cornmeal, sugar, baking powder, salt and granulated garlic. Process to combine.
Scatter the cold butter over the top of the dry ingredients. Pulse just until the butter is incorporated and cut into pea-sized pieces, about 7-10 pulses. Sprinkle ¾ cup of the shredded cheese and the scallions over top. Pulse just to incorporate, about 3-4 pulses.
Pour in the milk and egg mixture and pulse again until the dough starts to come together about 5-7 pulses. Don’t over-mix at this point—the dough will still look floury but should hold together when pinched. If the dough is too dry, drizzle in a bit more milk and pulse to combine.