Before you even think about boiling, you need to clean those gizzards. Most store-bought ones come pre-cleaned, but give them a rinse anyway. Trust me. You don’t want any surprise sand or grit in your final dish.
Next, slice off that little silver skin on the outside. It’s a thin membrane, and it’s not poisonous, but it stays chewy like a piece of bubble gum that lost its flavor. Cut it off. Your jaw will thank you later.
Some people like to slice the gizzards in half before boiling, while others leave them whole. I say: go whole for a classic boil, then slice after. It’s less fuss and helps them stay juicy. You do you, though.