Squeeze the juice of one lemon into a large bowl of water.

Rinse artichokes thoroughly.

To trim an artichoke: cut the stem leaving only an inch. Use a knife to cut the top one inch of the artichoke. Use scissors to cut any remaining sharp tips. Cut the artichoke into quarters. Remove the choke and inner leaves. Place artichoke in lemon water to help keep the artichoke from oxidizing. Repeat with remaining artichokes.

Bring a large pot of water to boil. Add prepared artichokes to boiling water, cover and cook for 15 - 20 minutes or until tender. Use a slotted spoon to transfer them to a plate.

Heat a grill to medium high heat.

Brush the artichokes with canola oil. Sprinkle with summer savory and salt. Place cut side down on the grill and grill for 7 -8 minutes or until dark grill marks appear. Transfer to a serving platter, sprinkle with Parmesan cheese and serve immediately.