Using a sharp knife, cut off approximately the top third of each artichoke. Remove the small tough leaves around the bottom and trim the stem, leaving approximately 1 inch attached.
Place each artichoke on a sturdy cutting board and carefully cut it in half lengthwise.
Using a small spoon, remove the fuzzy inner choke and the small purple-tipped inner leaves. Be careful not to remove the tender heart underneath.
Place the artichoke halves in a steamer basket and steam for approximately 20–25 minutes, or until the heart can be pierced easily with a knife.
While the artichokes are cooking, combine olive oil, minced garlic, lemon juice, lemon zest, Italian seasoning, salt, pepper, and red pepper flakes in a small bowl.
Preheat an outdoor grill to medium-high heat, approximately 400–450°F (200–230°C).
Clean and lightly oil the grill grates to help prevent sticking.
Pat the steamed artichokes dry. Brush both sides generously with the garlic-lemon olive oil mixture.
Grill for approximately 5–7 minutes, or until attractive grill marks and lightly charred edges develop.
Transfer the grilled artichokes to a serving platter. Sprinkle with freshly grated Parmesan and chopped parsley.
Serve immediately with plenty of fresh lemon wedges and the optional dipping sauce.