Heat a large skillet over high. Pat pork chops dry and season generously on both sides with salt and pepper. Add 1 tablespoon oil to skillet and swirl to coat. Add chops and cook until golden brown and meat has some give when pressed with your finger, about 4 minutes per side, flipping once. Transfer chops to a serving platter, cover loosely with foil, and let rest 5 minutes.
Wipe skillet clean and heat over medium-high. Add 2 tablespoons oil, green beans, scallion whites, and ginger. Cook, stirring occasionally, until ginger and scallions are soft and green beans are crisp-tender, 3 minutes. Season with salt and pepper. Add jalapeno (if using) and scallion greens and cook, stirring frequently, 1 minute. Add peppers and cook until warmed through; season with salt and pepper. To serve, top chops with vegetables.