Prepare a gas grill for direct grilling over medium heat (375°–400°F/190°–200°C). If using a charcoal grill, create two fire zones, one at medium heat and one at medium-high heat (475°–500°F/250°–260°C). Remove the lamb chops from the refrigerator 20–30 minutes before grilling.

Brush the grill grates clean. Halve the peppers lengthwise and seed them. Turn them skin side down, then brush the insides lightly with oil and sprinkle with salt. Place the peppers, cut side down, over direct medium heat on the grill and close the lid. Grill, turning occasionally, until lightly charred in places and somewhat softened. Transfer them to a serving plate and drizzle with the balsamic vinegar and a glug or two of your best olive oil. Season with a pinch of salt and a few grindings of pepper and arrange a few herb sprigs on top. Let the peppers rest while you grill the lamb.

If using a gas grill, raise the heat to medium-high (475°–500°F/250°–260°C).

Rub 2 tablespoons oil into all sides of the lamb chops. Season the chops generously with salt and pepper on all sides. Place the chops on the grill over direct medium-high heat, close the lid, and grill for 4 minutes. Turn the chops, close the lid again, and grill for 5 minutes longer, or until an instant-read thermometer inserted into the center of a chop away from bone registers 125°F (52°C) for medium-rare. Transfer the chops to a plate or cutting board and let rest for 5 minutes.

Arrange the lamb chops on the platter alongside the peppers. Scatter a few herb sprigs on top and serve.