Fill a large bowl with cold water and squeeze juice of 1 lemon into it. Begin preparing artichokes by removing tough outer leaves until you reach pale green tender ones. Cut off top third of each artichoke and trim stem to 1 inch.

Using a melon baller or small spoon, carefully remove the fuzzy choke from center of each artichoke, creating a cavity. Immediately place cleaned artichokes in lemon water to prevent browning.

Toast pine nuts in a dry skillet over medium heat until golden, shaking frequently. Let cool and roughly chop. In a bowl, combine breadcrumbs, pine nuts, half the garlic, parsley, mint, capers, 3 tablespoons olive oil, salt, and pepper.

Remove artichokes from water and pat dry. Gently spread leaves and fill cavities with breadcrumb mixture, pressing down lightly. Also tuck some filling between the leaves.

In a heavy-bottomed pot wide enough to hold artichokes upright, heat remaining olive oil over medium heat. Add remaining garlic and sauté until fragrant, about 1 minute.

Arrange stuffed artichokes upright in pot. Add wine and let it reduce by half. Add warm broth to reach halfway up artichokes. Cover tightly and simmer on low heat.

Continue braising covered for 45-50 minutes, checking liquid level every 15 minutes and adding more broth if needed. Artichokes are done when outer leaves pull away easily and hearts are tender when pierced.