Place the garlic in a jar or container that just holds them and cover with water. Retain the garlic in the jar and pour the water into a measuring cup. Note the amount. Discard half the water and add an equal quantity of the vinegar. Set aside.
In a medium saucepan over medium-high heat, place the sugar and 1 tablespoon of the water. Do not stir; instead, swirl the pan lightly and heat the mixture for 4 to 6 minutes until a light amber caramel forms.
Add the garlic cloves and salt to the saucepan and stir to coat the garlic with the caramel. Cook for 2 minutes, until the caramel turns slightly darker.
Add the reserved water and vinegar mixture to the saucepan. Reduce the heat to medium and simmer for 15 to 20 minutes, until the liquid reduces to a syrupy consistency and the garlic is soft. Taste the pickling liquid and reseason as necessary. Remove from the heat and set aside to cool to room temperature.
Transfer the mixture to a large food-safe plastic container. Weigh down the garlic cloves as needed to keep them submerged in the liquid. Seal the container. Store in the refrigerator for 2 to 4 days or until pickled. Serve cold.