In a medium saucepan, combine fresh or frozen blackberries with water and cook for 8–10 minutes, or until the berries have softened and released their juices.
From the softened blackberry mixture, a fine mesh sieve is used to remove seeds for a silky texture.
In a separate skillet, heat olive oil over medium heat. Add the minced garlic and sauté for about 1 minute until fragrant but not browned.
Return the strained blackberry puree to the saucepan. Stir in ketchup, apple cider vinegar, brown sugar, honey or maple syrup, and the sautéed garlic. Mix until well combined.
Stir in Worcestershire sauce, smoked paprika, and lemon juice. Season with salt and black pepper to taste.
Bring the mixture to a gentle simmer. Cook uncovered on low heat for 15–20 minutes, stirring occasionally, until the sauce thickens and the flavors meld together.
Now transfer the mixture into a blender or food processor. Blend until smooth.
Taste and adjust sweetness, tang, or smokiness as needed. Let the sauce cool slightly before storing it in a clean jar or airtight container.