Success! I finally got exactly what I wanted and it wasn't pickled garlic at all. I think that I have invented candied garlic, at least I couldn't find any recipes for it on the internet. What I wound up with today, thanks to the help of @AAQuesada, @MokaPot, and @lemniscate was the perfect garlic snack.
Candied Garlic
2 heads of garlic, peeled
1 cup water
1/2 cup sugar
2 tablespoons dark soy sauce
1 tablespoon Chinese black rice vinegar
15 G ginger, sliced thinly
1 star anise
Peel the garlic and place in the freezer overnight. Remove the next day and thaw completely.
Combine the ingredients for the syrup in a small saucepan and bring to a boil stirring until the sugar dissolves. Reduce the Heat and simmer very slowly for 30 minutes. Add the thawed garlic and continue to simmer for 15 minutes. Let the garlic cool in the syrup and it is ready to eat.
Note: I suppose that this could be made with regular rice vinegar but the black vinegar gives it in rich, smoky flavor. I suppose that if I just had the rice vinegar that I would add a drop of smoke flavoring.
This is the vinegar that I used.
