Preheat the grill to its highest setting.
Heat olive oil in a wide heavy-based pan and fry the shallots, garlic, and chorizo until soft.
Add wine and mussels, cover with a lid, and cook for 2-3 minutes until mussels open.
Discard any unopened mussels and remove the rest from the pan, reserving the juices.
Remove and discard the top shells and arrange the mussels on a baking sheet.
Add vinegar, thyme, and salt to the pan and reduce until a thick sauce forms.
Spoon the reduced sauce over the mussels.
Mix butter, breadcrumbs, and cheese in a bowl and spoon over the mussels.
Grill until golden-brown and serve on a bed of baby watercress.