Cut artichoke hearts into even pieces. Dice ham, discarding any excess fat.
Heat 2 tablespoons oil in a nonstick pan. Add garlic, cook, stirring, just until transparent. Add artichoke pieces and wine. Cook over high heat, covered, 2 minutes. Add ham and herbs; heat briefly. Set pan aside and let mixture cool to lukewarm. Transfer to a serving bowl.
Add beans, tomatoes and rocket to artichoke mixture. Add salt, pepper and remaining lemon juice and oil to taste.
The globe artichoke is the large flower bud of a bushy thistle plant. Its edible portions are the buttery heart and the earthy-tasting fleshy part at the base of the outer leaves. Steaming, boiling or baking are the best cooking methods.