Bring apple cider vinegar to a boil in a small saucepan. Reduce heat to medium-low and stir in maple syrup; cover and cook for 10 minutes.
Mix cold water and quick-mixing flour together in a small bowl. Whisk into the maple syrup mixture. Stir in 2/3 cup brown sugar and cook until sauce thickens, about 5 minutes. Cover and keep warm.
Season pork chops with salt and pepper on both sides.
Heat olive oil and butter in a large skillet over medium-high heat. Add pork chops; cook until browned, about 4 minutes. Flip with tongs; sprinkle 1 teaspoon brown sugar over each chop. Continue cooking until second side is browned, about 4 minutes more. Transfer to serving plates and spoon sauce on top.