Trim the artichokes by cutting off the stem and the top third of each artichoke. Remove the tough outer leaves and snip off any sharp tips from the remaining leaves.
Cut the artichokes in half lengthwise and scoop out the fuzzy choke with a spoon.
Bring a large pot of salted water to a boil. Add the artichoke halves and cook until tender, about 15 minutes. Drain and let cool slightly.
In a small bowl, mix together olive oil, lemon juice, parsley, and minced garlic.
Preheat the grill to medium-high heat.
Brush the artichokes with the olive oil mixture, making sure to get between the leaves.
Place the artichokes on the grill, cut side down, and grill for 5-7 minutes or until they have nice grill marks.
Flip the artichokes and grill for an additional 5 minutes.
Serve warm, with additional olive oil mixture for dipping if desired.