It is basically a grilled ham and cheese sandwich with a thin filling of sottaceti (soet-tah-CHEH-tee,) or pickled vegetables. If you'd like to make your own, you should obtain a jar of giardiniera, then drain (but do not rinse) the veggies. You may pick and choose what veggies to include and in what proportion: for example, in the pictured jar, I find the amount of cauliflower rather alarming. Mince them coarsely. Prepare your usual grilled ham and cheese, but about midway, re-open the sandwich and spread filling on one side. Continue to cook until done to your liking.
Italians generally do not make this either with prosciutto or with crusty bread.