In a saucepan, heat the 3 tablespoons of vegetable oil. Add the garlic and cook over moderately low heat, stirring, until just golden. Add the chopped onion and cook over moderate heat, stirring, until softened and just starting to brown, about 7 minutes.
Stir in the paprika & tomato paste and cook until glossy, about 2 minutes.
Add the blackberries, vinegar, brown sugar, soy sauce, chipotles, mustard and cumin and bring just to a boil. Simmer over moderately low heat, stirring, until slightly thickened and the berries are very tender, about 20 minutes.
Transfer the sauce to a blender and let cool slightly, then puree until smooth. Strain through a fine sieve into a bowl, discarding the solids. Season the sauce with salt and pepper and let cool completely.