Heat the oven to 500°F and position the rack in the lower third. Generously grease a 9 by 13–inch baking dish with olive oil. Put the tomatoes in a strainer set over a bowl and drain. Taste the tomatoes and sprinkle with salt if necessary and some pepper. Drain, shaking occasionally, while you prepare the other ingredients.
Put the flour, baking powder, and 1 teaspoon salt in a large bowl and stir to combine. Add the 1/3 cup olive oil and 3/4 cup warm water, and mix just until the dough comes together (it should still be a little crumbly). If the dough is too dry, add water 1 tablespoon at a time and stir briefly after each addition. In the unlikely event the dough is too wet, add 1 tablespoon flour and stir.
Press the dough into the prepared pan all the way to the edge, making sure it’s the same thickness everywhere. Scatter the drained tomatoes over the dough, leaving a 1/2-inch border all around, then sprinkle the cheese over the tomatoes. Transfer the pan to the oven and bake for 10 minutes.
Carefully put the pepperoni on the pizza and continue baking until the crust is golden and the cheese bubbles, another 3 to 5 minutes. Sprinkle with the herbs and red chile flakes and cool for at least 5 minutes before cutting into squares and serving.