Massage the rack of lamb with the olive oil and garlic - place into a resealable plastic bag to marinade. Place 3 sprigs of the rosemary under the rack of lamb and 3 on top of the rack of lamb. Marinate for at least 2 hours or up to 8 hours in the fridge. Bring to room temperature before cooking.
Preheat your oven to 375 degrees. Place the rack of lamb in a cast iron skillet, foil lined baking sheet, or roasting pan.
Lay the 3 rosemary sprigs under the roast and 3 on top of the roast, like you did when marinating (you can use the same ones).
Generously season the rack of lamb with salt and pepper. Roast for 20-30 minutes, depending on how done your like your lamb. The internal temperature should reach 130-140 for medium rare.
Turn the oven up to broil for a couple minutes to put a char on the outside if you desire. Remove from the oven and let it rest for 5 minutes before slicing.