Bring a large pot of salted water to a boil. Trim stem of each artichoke to 1 inch, and snap off dark outer leaves. Use a sharp knife to trim off the top inch from the artichoke leaves. Use a paring knife to peel the dark green skin from the stem and base of artichoke. Slice each artichoke in half lengthwise. Use a paring knife to remove the choke and the purple, prickly-tipped leaves from center of each half. Place prepped artichokes in a large bowl of cold water with juice of 2 lemons.

Drain artichokes, and cook in boiling salted water until just tender when pierced with a sharp knife, about 12 minutes. Drain artichokes, and pat dry.

Heat a gas grill to medium-high. Carefully wipe the preheated grates with a lightly oiled paper towel.

Toss artichokes in oil. Grill artichokes, cut sides down, uncovered, over direct heat, turning occasionally, until tender and lightly charred in spots, about8- 10 minutes. Halve remaining lemon. Grill lemon, cut sides down, and chile until charred and softened, about 5 minutes.

Squeeze juice from warm grilled lemons into a bowl, discarding seeds. Scoop out lemon flesh, coarsely chop, and add to juice. Whisk in mayonnaise, yogurt, mint, garlic, and salt. Serve warm artichokes with aioli and grilled bread.