Halve the tomatoes and quarter the onion. Leave the garlic cloves whole. Place them on a grill rack over medium heat and grill for 10-15 minutes, or until slightly softened and lightly charred.
Heat the olive oil in a saucepan over medium heat. Add the grilled tomatoes, onion, and garlic. Sauté for another 5 minutes to intensify the flavors.
Add the brown sugar, apple cider vinegar, smoked paprika, chili flakes, salt, and pepper. Mix well, and cook for 15 minutes over medium heat, until the tomatoes are completely broken down.
Pour in the soy sauce and BBQ sauce, then cook for another 5 minutes to allow the flavors to meld.
Let the mixture cool slightly, then purée in a blender or with an immersion blender until completely smooth.
Strain through a fine-mesh sieve for an even silkier texture.
Let it cool completely, then pour into sterilized jars. It will keep in the refrigerator for up to a week.
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