Set grill to high. Brush tomato halves with the first amount of olive oil and sprinkle with the first amount of garlic. Place tomatoes and onion quarters cut side down on hot grill. Cook until lightly charred on all sides. Cool slightly and roughly chop onions.
Heat second amount of oil in a saucepan over medium-low. Add charred onion and celery and cook until softened. Add charred tomato, vinegar, sugar, tomato puree, salt, the second amount of garlic, allspice, thyme, and smoked paprika. Stir until well mixed. Bring to a boil and reduce heat to low and cook for 40 minutes.
Cool slightly. Transfer to a blender and blend until smooth. Hold refrigerated until needed.
This is a perfect housemade condiment for any bar or pub snack, but delicious with this Carrot Hotdog recipe.
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