Peel, core, and dice quinces and apples; chop onion and mince garlic.
Put diced fruit in a saucepan and cover with water; simmer 25–30 minutes until fully soft. Drain well and reserve 200 ml of the cooking water.
Heat olive oil in a wide pan over medium; cook onion 8 minutes until soft and lightly golden. Add garlic and cook 1 minute.
Stir in tomato paste, mustard, smoked paprika, ginger, allspice, and cinnamon; cook 30 seconds, stirring.
Add softened fruit, apple cider vinegar, brown sugar, honey, soy, Worcestershire, tamarind, salt, pepper, and the 200 ml reserved water; bring to a gentle simmer.
Cook uncovered 40–45 minutes on low, stirring occasionally, until thickened and amber-brown.
Blend smooth (stick blender or jug). Add a splash of hot water if too thick.
Push the warm puree through a fine sieve for a silky texture.
Return to the pan and simmer on low 20–25 minutes, stirring often, until it coats the back of a spoon and deepens in colour.
Taste and adjust salt or vinegar. Ladle hot ketchup into sterilised bottles/jars and seal. Cool, then refrigerate.