Wash and pat dry the lamb chops. Mash the garlic cloves with roughly a pinch of salt. Rub the chops with the garlic mixture and season with salt and pepper.
Mix the oil with the rosemary and thyme until combined (use a hand mixer for 30 seconds if needed to break up the herbs). Brush the lamb chops with this seasoning oil, place in a bowl, pour the remaining oil over them, cover, and refrigerate for 1 hour.
Wash and trim the carrots. For larger carrots, cut crosswise in half, then halve or quarter lengthwise. Melt the butter in a wide pan with a lid over medium heat. Add the carrots and lightly brown for 10 minutes. Cover the pan and cook for about 10 minutes until tender. Add the hot broth, sugar, and a pinch of salt. Simmer uncovered until the liquid completely evaporates and coats the carrots.
Remove the lamb chops from the marinade and drain well. Grill on high heat for 3–4 minutes on each side, aiming for pink centers. While grilling, finely chop the chives.
Wrap the grilled lamb chops in aluminum foil and let rest for 2–3 minutes so the juices redistribute. Scatter the chives over the carrots.
Arrange the lamb chops on preheated plates with the glazed carrots. Serve immediately with crispy, golden-brown french fries.