Trim all visible fat from the gizzards. Rinse well.
Cut each gizzard into three or four pieces.
Place the gizzards in a medium-sized non-aluminum saucepan or skillet.
Pour the vinegar over them. Add the garlic, bay leaf and cracked black pepper.
Set over high heat and bring to a boil without stirring.
Let boil for a minute or two before stirring and adding the sliced shallots.
Add about 2 cups of water, lower the heat, cover and simmer for an hour or longer until the gizzards are tender.
Add more water, if necessary, but the remaining liquid should only be a few tablespoonfuls by the end of the cooking time.
Meanwhile, wash the kangkong and trim, discarding the tough lower portion of the stalks. Cut into two-inch lengths.
When the gizzards are done, turn up the heat and add the soy paste. Let boil for about 30 seconds before adding the kangkong. Don’t worry if the adobo looks quite dry at this point; the kangkong will expel water after a few minutes.
Toss the gizzards with the kangkong. Lower the heat, cover and simmer for 2-3 minutes.