Preheat the oven to 200C/400F/Gas 6.
Prepare the lamb by piercing the leg eight times using a small sharp knife. Into each hole push down a garlic clove, a sprig of rosemary and a sprig of thyme. Brush the basil pesto over the meat before seasoning with salt and freshly ground black pepper. Place into an oven tray and drizzle with olive oil.
Place the tray into the oven for 45 minutes to an hour, or until cooked to your liking. Once cooked, remove from the oven and cover with aluminium foil. Leave to rest for 20 minutes.
For the minted potatoes, bring a large pan of water to the boil. Place the potatoes into the water with the bouillon, a little salt, thyme, mint, bay leaves and garlic and bring back to the boil.
Once the potatoes are cooked, drain and discard the cooking liquid, herbs and garlic. Return the potatoes to the pan, add the butter and chopped mint and season with salt and freshly ground black pepper.
To serve, carve the lamb and place onto serving plates along with the minted new potatoes.