Cut the stem off at the base of the artichoke. With a chef’s knife, cut off the top 1/3 or so of the artichoke, so all pointy ends are removed from the top (or you can cut each tip off with scissors, if you prefer).
Mix salt, rosemary & minced garlic, and place mixture between layers of leaves.
Put remaining ingredients in a deep saucepan and add artichoke. Bring to a simmer, cover, and cook for 45 to 50 minutes, or until leaves are very tender.