Ground sumac (a tangy Middle Eastern spice; optional)
Heat the oil in a large-ish pot (5 or 6 quarts) over medium heat. Add the garlic and cook, stirring, until fragrant and lightly browned, 3 to 4 minutes. Add the water and vermouth, then juice the lemons right into the pot and throw the juiced lemons into the pot.
Bring the liquid to a boil, reduce the heat to a simmer, add the artichokes to the pot, cover, and simmer until the artichokes are tender and a leaf pulls away easily, 25 to 30 minutes.
Drain, cool slightly, then serve the artichokes with a dollop of aioli and a little sumac sprinkled on top.