Bring a large pot of salted water to a boil. Add the artichokes and cook over medium-low heat for 15 minutes. Remove from the heat and drain.
Preheat the oven to 325°F.
Add the basil, thyme, sorrel, and garlic to a small bowl. Slowly add the olive oil and whisk to combine.
Place the artichokes in a small baking dish. Gently stuff the herb mixture underneath and in between the artichoke leaves and sprinkle a little over the top. Drizzle with the lemon juice and season with sea salt. Put the artichokes in the oven and cook for 1 hour. Remove from the oven.
Transfer the artichokes to a serving platter. Drizzle a little olive oil over the top and serve immediately with the lemon wedges.