These appetizer or side-dish morsels are a nod to the classic Roman-Jewish preparation carciofi alla giudia, but with a lighter twist: They're roasted instead of deep-fried.
Caper aioli: Preheat oven to 500 degrees with a rimmed baking sheet on a rack in lowest position. Puree yolk, lemon zest and juice, garlic, and capers in a blender until smooth. With motor running, gradually add oil in a steady stream until mixture is thick and creamy. Season generously with salt and pepper. Transfer to a serving bowl; garnish with more capers.
Artichokes: Squeeze lemon halves into a large bowl of water; add rinds. Working with 1 artichoke at a time, remove all tough outer leaves. With a serrated knife, cut off top 1/2 inch; with a paring knife, trim and peel stem. Open soft inner leaves with your fingers until artichoke resembles a flower in full bloom. (Transfer to lemon water as you work to prevent discoloration.) Drain artichokes upside down, with leaves spread open on paper towels.
Toss artichokes with oil. Place upside down on hot baking sheet and roast, stirring once halfway through, until leaves are crisp and hearts are tender, 8 to 13 minutes. Season with flaky salt and serve immediately, with aioli.