Preheat oven to 400 degrees F.
Using a small bowl, combine 1/4 cup olive oil, the minced garlic, rosemary and thyme.
Score the fatty side of the lamb to about 1/4" deep. Season with salt and pepper.
Using a large rimmed baking sheet, scatter the whole garlic cloves, onions, potatoes, carrots and celery, drizzle them with olive oil. Season with salt and pepper. Scatter the sprigs of rosemary over the vegetables and set the leg of lamb on top., fatty side up. Spread 1/2 of the garlic and herb mixture all over the lamb, be sure to rub it into the score lines. Roast for 20 minutes.
Spread the rest of the garlic and herb mixture over the lamb and add 1/4 cup of vegetable broth to the baking sheet. Roast the lamb for about 1 hour and 15 minutes longer, rotate the baking sheet several times during that period. If at any point during the cooking process if the vegetables start to get dark add a few tbsp more vegetable broth.
Cook until an instant read thermometer inserted in the thickest part of the meat reads 145 degrees F. Transfer the lamb to a carving board to rest for 20 minutes. Discard the rosemary sprigs. Slice the lamb into 1/2" thick slices and serve with the roasted vegetables.