How to Make It
In a small bowl, combine the garlic with 3/4 teaspoon of salt; mash to a paste with the back of a small spoon. Stir in the lemon juice and mayonnaise until smooth. Gradually whisk in 1/4 cup of the olive oil in a thin stream until the aioli is emulsified. Refrigerate the aioli until serving.
Bring a large saucepan of salted water to a boil. Add the artichokes, cover with a lid slightly smaller than the saucepan to keep the artichokes submerged and cook until the bottoms are tender, about 15 minutes. Drain the artichokes and spread them out on a large plate to cool slightly. Pull off the tough outer leaves and cut each artichoke in half. Pat dry.
In a large skillet, heat 2 tablespoons of the olive oil until shimmering. Add the artichokes and cook over high heat, stirring occasionally, until golden and crisp, 4 to 5 minutes. Season with salt and pepper and sprinkle with the chopped parsley. Transfer the artichokes to a platter and keep warm.
Heat a cast-iron grill pan or large skillet. Rub the tuna with the remaining 1 tablespoon of olive oil and season with salt and pepper. Grill the tuna over high heat, turning once, until browned and the meat is medium rare, about 3 minutes total. Transfer the tuna to the platter and serve immediately with the aioli and lemon wedges.