Fill a large pot with 4 quarts water and bring to a boil over high heat; add 1 tbsp kosher salt, then reduce to a brisk simmer.
Halve the lemon. Working with one artichoke at a time, snap off the tough outer leaves until the pale green leaves are exposed, trim the top by about 1 inch, and pare the stem, leaving about 1 inch attached; cut the artichoke in half lengthwise and scoop out the fuzzy choke. Rub cut surfaces with the halved lemon as you go, then drop the squeezed lemon halves into the simmering water.
Add the prepared artichoke halves to the pot and simmer until the base yields to a knife tip and outer leaves pull with slight resistance, 20–25 minutes.
Drain the artichokes well in a colander, cut side down, 5 minutes. Pat dry. Meanwhile, preheat a grill to medium-high heat (400–450°F).
In a bowl, whisk together the olive oil, lemon juice, minced garlic, chopped parsley, 0.5 tsp kosher salt, and 0.25 tsp freshly ground black pepper.
Brush the cut sides and outsides of the drained artichokes with about half of the oil mixture.
Clean and lightly oil the grill grates. Place artichokes cut side down and grill until well-marked and lightly charred at the edges, 3–5 minutes, until you smell a toasty aroma.
Flip artichokes, brush with remaining oil mixture, and grill until the hearts are hot and edges crisp, 2–4 minutes more.
Transfer to a platter and rest 2 minutes so juices settle.