Ingredients

1. 12 fresh uncleaned squid of even size (about 3 pounds)
2. 2 cups dry bread crumbs
3. 2 eggs, lightly beaten
4. 3 garlic cloves, 2 finely chopped and 1 minced
5. 1 small onion, finely chopped
6. 1/2 cup plus 1 teaspoon finely chopped fresh flat-leaf parsley
7. 3 tablespoons milk
8. 6 tablespoons extra-virgin olive oil
9. 1/2 cup freshly grated Pecorino or Parmigiano-Reggiano cheese (see Note)
10. 2 canned plum tomatoes, drained and chopped
11. 8 large green olives, pitted and coarsely chopped
12. Salt and freshly ground pepper
13. 1/2 cup dry white wine plus more if needed
14. Lemon wedges, for serving

Directions

1. Clean the squid: rub the thin purplish membranes off with your fingers, being careful to keep the bodies and hoods attached. (It isn't necessary to remove all the scraps but the squid will be more attractive without them.) Set the squid on a cutting board and cut a slit in the hoods from the base to the top, leaving the tentacles attached. Pull out and discard the innards, including the bony strip called the beak. Rinse the squid thoroughly inside and out; set aside to drain. Using scissors or a sharp knife, remove the very long tentacle and the fanlike fins (on either side of the hood) from each squid; chop them into small pieces.
2. In a medium bowl, mix the bread crumbs with the eggs, finely chopped garlic, onion and 1/3 cup parsley. Add the milk and 3 tablespoons of the olive oil to form a moist paste. Mix in the cheese, tomatoes, olives and the reserved chopped squid and season with salt and pepper. Stuff each squid hood loosely with the mixture. 
3. In a nonreactive skillet large enough to hold all the squid in a single layer, heat the remaining 3 tablespoons olive oil. Add the minced garlic and the remaining 3 tablespoons parsley and cook over moderate heat just until the garlic is opaque, about 30 seconds. Add the stuffed squid to the pan in a single layer and cook until browned, about 3 minutes per side. Add the wine to the pan, cover and reduce the heat to low. Cook until the squid is tender, about 30 minutes; if the pan begins to look dry, add a little more wine. 
4. Spoon the small amount of sauce over the squid and serve immediately, with lemon wedges.

Notes

The cheese used in Apulia, though called Pecorino, is a mixture of ewe's and cow's milk. It is not the sharp cheese known as Pecorino Romano. If you can't find Pecorino from Apulia, Sardinia or Tuscany, use Parmigiano-Reggiano instead.