Preheat oven to 475 degrees. Form dough (as directed in Basic Pizza Dough recipe) in a 9-by-13-inch rimmed baking sheet. Arrange eggplant lengthwise on dough, 3 slices side-by-side on top half, 3 on bottom half; press into dough. Drizzle with oil, and sprinkle with salt and red-pepper flakes.
Bake until cooked through and crust is golden on edges and bottom, about 18 minutes.
Using a metal spatula, slide pie onto a cutting board. Sprinkle with pistachios, feta, pomegranate seeds, and cilantro. Slice into 6 pieces and serve.