Place the blackberries and water in a large saucepan. Bring to a boil, then lower the heat and simmer for 5-10 minutes until the blackberries have softened. Use an immersion blender to puree the blackberry mixture (or, carefully pour into a blender or food processor and pulse until pureed). Pour the blackberry puree through a medium-mesh sieve to remove the seeds. Discard the seeds and pulp, and set the seedless puree aside.
Rinse out the saucepan and place back on the stove. Add in the oil and heat over medium heat. Add in the chopped onion and sauté until softened and translucent. Add the minced garlic and sauté for about a minute, or until fragrant.
Pour the strained berry liquid back into the pot, and add all of the other ingredients except for the gochujang (molasses, brown sugar, tomato sauce, apple cider vinegar, thyme, Worcestershire sauce, and salt). Bring to a simmer over medium heat. Continue to cook for about 15 minutes until the sauce has thickened and can coat the back of a spoon.
Add in 1 to 2 tablespoons of gochujang, depending on the level of spice you like. Use an immersion blender (or regular blender/food processor) to puree the sauce until completely smooth. Strain again if you want an extremely smooth sauce. Taste the sauce and adjust the seasoning if necessary.
Transfer the sauce to a jar or bottle. Keep in the refrigerator for up to two weeks. Freeze for up to 3 months.