Combine olive oil, black olives, lemon juice, apple cider vinegar, garlic, capers, fresh parsley, dried thyme, and sea salt in a high-speed blender or food processor.

Blend on low or pulse setting for 10-15 seconds until combined into a chunky paste.

Add more olive oil if a thinner consistency is desired.

Serve immediately for the freshest flavor, or store covered in the refrigerator for up to 2 days.

If refrigerated, stir briskly before serving to combine ingredients again.