In a saucepan, bring to a boil the vinegar, sugar, water, garlic, and carrot. Boil for 3 minutes to thicken to a syrup.
Mix one tablespoon cornstarch with one tablespoon water, then add the cornstarch mix, sambal oelek, and fresh ginger to the boiling syrup. Boil for an additional 3 minutes while stirring often.
Remove from heat and allow the chili sauce to cool to room temperature. Then remove the garlic cloves.
Serve immediately or, for best flavor, refrigerate overnight to allow the ingredients to fully meld.