Set grill to high. Brush tomato halves with first amount of olive oil and sprinkle with first amount of garlic. Place tomatoes and onion quarters cut side down on hot grill. Cook until lighlty 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, 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 house made condiment for any bar or pub snack, but delicious with this Carrot Hotdog recipe.