Place a large cast-iron skillet over medium-high heat until hot. Once hot, add the olive oil. Season lamb ribs with salt and pepper on both sides. Add them to the pan. Sear on both sides until golden-brown and cooked through, about 5-7 minutes per side.
Transfer to a plate and cover with foil.
Reduce heat to medium and add minced garlic and sauté it just until fragrant, for about 30 seconds.
Add fresh rosemary, stir and cook for 30 seconds. Add brown sugar and broth. Stir until the sugar has completely melted. Season with salt and pepper to taste.
Increase heat to medium-high, stir and cook the sauce until it reduces and thickens slightly about 5 minutes.
Add lamb ribs back to the pan, baste with the sauce, add a few sprigs of fresh rosemary and transfer to the oven for about 7-10 minutes. Broil for 1-2 minutes before serving.