Prepare the artichokes by cutting them in half from top to bottom, through the core. Using a small spoon, remove the fuzzy center. Peel the outside skin from the stems and if you like, trim the ends off the outside leaves (but you can leave if you like, you just can't eat anything from that part).
Boil or steam the artichokes until tender, around 20 minutes. Drain then toss with the olive oil, lemon juice, basil and garlic.
You can either grill them straight away or leave them to take on the flavors a bit more. When ready to grill, warm the grill then cook a couple minutes either side until lightly charred.
Enjoy as they are or also good with a little aioli or other mild dip/sauce to dip in.To eat them, you peel off the leaves and pull away the flesh from the bottom with your teeth. As you get closer to the middle, you'll get more tender flesh then you can eat the heart.