Season chops with 1 tablespoon salt and 1/2 teaspoon pepper total. Heat 1 tablespoon oil in a large skillet over medium-high heat. Cook chops, flipping once, until golden brown on both sides, about 5 minutes total. Transfer to a plate.
Reduce heat to medium and add remaining tablespoon oil to skillet. Cook peppers, onion, and basil, gently stirring occasionally, until vegetables soften and turn golden in places, about 7 minutes. Return chops along with any accumulated juices on plate to skillet, placing them on top of vegetables. Add vinegar, cover, and cook until a thermometer inserted into thickest part of chops (do not touch bone) reaches 145 degrees, about 3 minutes.
Discard basil sprigs and divide chops and vegetables evenly among 4 plates. Garnish with basil leaves.