Peel and thinly slice onions evenly.
Heat 3 tbsp olive oil in a heavy-bottomed pan over low–medium heat. Add onions and cook 25–30 minutes, stirring often, until deep golden.
While onions cook, peel, core, and dice quince into ≤1 cm cubes.
When the onions are finished, stir in diced quince, mustard seeds, salt, and pepper. Cook 5 minutes, stirring often, until quince starts to soften and becomes aromatic.
Sprinkle in brown sugar and pour in apple cider vinegar; stir to dissolve. Reduce heat and simmer uncovered 40–50 minutes, stirring occasionally, until thick and jammy.
Drag a spoon across the pan; if it leaves a clear path that slowly fills in, it’s ready. Chunks should hold their shape; mash lightly if you prefer it smoother.
Spoon hot chutney into sterilised jars, seal immediately, and cool. For best flavour, let mature at least 1 week before opening.