In a heavy pot, heat the olive oil. Add the chopped onion and garlic and cook until transparent. Add the blueberries to the onion mixture, cover, and cook until the blueberries soften, about 10 minutes.
Remove the lid and mash the blueberries. Add the apple cider vinegar, brown sugar, ground mustard, Worcestershire sauce, and unsweetened applesauce. Cook for five more minutes.
Puree the mixture with an immersion blender or pour the mixture into a blender and puree in batches. Season to taste with sea salt and fresh pepper. Store in the refrigerator.