Wash the tomatoes and cut them in half.
Preheat the grill to medium heat and place the tomatoes cut-side down on the grates.
Grill the tomatoes for 5-6 minutes, until slightly charred and smoky.
Meanwhile, finely chop the onion and garlic.
In a saucepan, heat the olive oil over medium heat, then sauté the onion and garlic for 3-4 minutes, until softened.
Add the grilled tomatoes, then stir in the BBQ sauce, smoked paprika, salt, and pepper.
Pour in the vegetable broth, then simmer over low heat for 10-15 minutes to allow the flavors to meld.
Blend the soup until smooth, then strain it through a fine-mesh sieve for a silky texture.
Before serving, garnish with fresh chopped basil and serve hot.
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