Grilled and Smothered Artichokes #WeekdaySupper

 3 medium-sized artichokes (stems attached), trimmed, peeled, quartered and choke removed

 Zest of 1 lemon

 2 large lemons, 1 halved and juiced, 1 quartered

 1 tablespoon balsamic vinegar

 1/2 cup extra-virgin olive oil

 2 garlic

 1/2 teaspoon fine sea salt

 1/8 teaspoon freshly ground black pepper, plus more to taste

 1/2 cup loosely packed fresh flat-leaf parsley leaves, coarsely chopped

 Coarse or flaked sea salt to taste, for finishing