Press the pizza dough into a greased 9- to 10-inch cast-iron skillet and let rise until doubled in size, 20 to 30 minutes.
Preheat the oven to 400 degrees. In a medium nonstick skillet, heat 1 tablespoon olive oil over medium heat. Add the garlic and cook, stirring, for 1 minute. Add the tomatoes, season with salt and black pepper and cook, stirring, for 1 minute more. Remove from the heat and let cool for a few minutes; discard the garlic.
Drizzle the remaining 1 tablespoon olive oil over the dough; spoon the tomato mixture on top, leaving a 1/2-inch border. Bake until golden and bubbly, about 25 minutes. Sprinkle the cheese, crushed red pepper and oregano on top and bake until the cheese is melted, about 5 minutes. Let cool in the pan for 20 minutes before serving.