Season the pork chops with salt and pepper. Sprinkle all over with one and a half tablespoons flour. Heat 1/2 tablespoon olive oil in a large nonstick skillet over medium-high heat. Working in 2 batches, add the pork chops and cook until golden and just cooked through, 3 to 4 minutes on each side, adding 1/2 tablespoon olive oil to the skillet between batches. Transfer the chops to a plate and keep warm.

Heat the remaining 1/2 tablespoon olive oil in the same skillet. Add the mushrooms, garlic, scallion whites and a pinch of salt and cook, without stirring, until the mushrooms begin to brown, about 3 minutes. Sprinkle in the remaining 1/2 tablespoon flour and cook, stirring occasionally, until the mushrooms are soft, about 3 more minutes. Stir in the chicken broth and sour cream, bring to a simmer and cook until the gravy thickens, about 1 more minute.

Divide the pork chops among the plates. Drizzle any juices from the pork into the gravy. stir in the scallion greens and parsley. Season with salt and pepper, spoon over the pork. Serve with cornbread.