Wash the tomatoes and cut them in half.
Preheat the grill to medium heat and place the tomatoes on the grill rack, cut-side down.
Grill the tomatoes for 5-6 minutes, until slightly charred and smoky.
Meanwhile, finely chop the onion and garlic.
Heat the olive oil in a saucepan over medium heat, then sauté the onion and garlic for 3-4 minutes, until softened.
Add the grilled tomatoes, then stir in the brown sugar, apple cider vinegar, BBQ sauce, smoked paprika, salt, and pepper.
Simmer over low heat for 15-20 minutes, allowing the flavors to meld and the sauce to thicken.
Blend the mixture until smooth, then strain through a fine-mesh sieve for a silky texture.
Let it cool completely, then pour into a sterilized jar and store in the refrigerator.
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