Place a large sheet pan in the oven, then preheat oven to 400 degrees F. Zest lemons into a medium bowl. Juice lemons into a large bowl, then add enough cool water to fill the bowl halfway.
Working one at a time, trim the bottom of the stem of each artichoke. Pull off dark outer leaves and stop when you reach the pale, very tender inner leaves. Cut off the top, prickly part of the artichoke, shave the rough parts off the base, and peel the stem. Halve the artichokes and place in the lemon water while you prep the remainder.
Drain artichokes and pat dry. Dry the large bowl. Return artichokes to bowl and add 3 tablespoons olive oil, 1 teaspoon salt, and ½ teaspoon pepper. Toss to coat. Carefully remove hot sheet pan from oven. Place artichokes on sheet pan, cut-side down. Roast until tender and golden on the bottom, about 12 to 15 minutes.
Meanwhile, add the feta, capers, mint, and ½ teaspoon pepper to bowl with lemon zest. Stir with a fork until well combined.
Using tongs, turn artichokes so that the cut side is up. Spoon feta filling on top of each and drizzle with 2 tablespoons olive oil. Continue to roast until very tender and filling is hot, about 5 to 7 minutes longer. Transfer to a platter and serve.
Photography by Robert Bredvad. Food and Prop Styling by Maeve Sheridan.