Fill a large pot with water and bring it to a boil.
To prepare the artichokes, trim off the tough outer leaves and cut off the top inch of the artichoke. Cut in half lengthwise and remove the fuzzy choke with a spoon or knife. Brush the insides of the artichokes with one half of the lemon to prevent it from browning.
Once the water is boiling, add the artichokes to the pot and cook for 10-15 minutes, or until they are tender when pierced with a fork. Drain the artichokes and let them cool slightly.
In a small bowl, combine the olive oil, breadcrumbs, Parmesan cheese, garlic, salt, pepper, and the juice of half a lemon. Mix well to combine.
Preheat your outdoor grill to medium-high heat.
Sprinkle the breadcrumb mixture between the leaves so that every crevice of the artichoke gets seasoned.
Place the artichokes on the grill, cut side down. Grill for 5-7 minutes, or until they are lightly charred and heated through.
Serve the grilled artichokes with lemon wedges on the side for squeezing over the top.