Preheat oven to 400 degrees. Brush an 8-inch square baking dish with oil. In a medium bowl, whisk together cornmeal, 1 cup flour, baking powder, and 3/4 teaspoon salt. Add milk, egg, and 3 tablespoons oil and whisk until combined. Transfer to baking dish and bake until a toothpick inserted in center comes out clean, 20 to 25 minutes. Let cool in dish on a wire rack. Crumble one-third the cooled cornbread onto a rimmed baking sheet (you should have 2 cups) and reserve for Cornbread-Stuffed Shrimp.
Meanwhile, in a large skillet, heat remaining 4 teaspoons oil over high. Season pork with salt and pepper and cook until browned and cooked through, 3 to 4 minutes per side. Transfer to a platter and loosely tent with foil. Reduce heat to medium, add onion, and cook until softened, 8 minutes. Add remaining 2 tablespoons flour and stir to combine. Gradually whisk in broth and bring to a boil, stirring constantly, 3 minutes. Add kale and cook, stirring, until wilted, 4 minutes. Serve sauce over pork chops, alongside remaining cornbread.
We use hearty greens, not cream, to bulk up the sauce for smothered pork chops.