Wash the key limes well and slice in half. Toss in a bowl with key lime juice and salt.
Make an incision in each half with the tip of a paring knife and insert a clove into each half.
Pack the cinnamon stick, peppercorns, start anise, and all the contents of the bowl into a glass jar. Seal and allow the key limes to ripen at room temperature for 7 days. Shake daily to distribute the salt and flavorings.
After 7 days, add the olive oil to top the jar and age 3-4 weeks before using. Store in the refrigerator for up to 6 months.