Preheat oven to 400 degrees F. Grease a 9x13-inch baking pan.
In a large bowl, whisk together the flour, garlic powder and oregano. Add the milk and eggs and gently stir until thoroughly combined. Add the pepperoni and cheeses and stir in with a wooden spoon or rubber spatula until evenly distributed.
Pour the mixture into the prepared baking dish and spread into an even layer. Bake until golden brown and bubbling, 30 to 40 minutes. Let sit for at least 15 minutes before cutting and serving.