Trim outer leaves and stems from artichokes, leaving just the tender yellow-green leaves. Drop artichokes into a bowl of ice water mixed with lemon juice and olive oil.
Bring a large pot of water to a boil and add salt. Drain artichokes and add to boiling water; simmer until tender, 10 to 20 minutes. Cut any larger ones in half, removing any fuzz at the heart.
Set a frying pan over medium-high heat. Add pancetta and stir until fat is rendered. Add garlic and stir until golden. Add wine and the baby artichokes. Cook until wine is almost evaporated. Add mint and salt and pepper to taste. Serve topped with grated parmesan cheese.