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Melt the membrillo and sherry together in a small pan until syrupy. Leave to cool slightly.
Cut the halloumi into long rectangular strips about 2cm wide, then in half again (where it naturally starts to separate) and thread onto thin skewers. Brush the halloumi generously with the glaze.
Oil the bars of a barbecue, then light it and wait until the flames have died down and the coals are ashy white, or use an oiled griddle pan to stop the halloumi from sticking, then grill or griddle for 1-2 mins on each side until golden and charred. Turn only after the pieces of halloumi release themselves from the grill and it’s easier to use tongs to pick up the cheese, rather than handling the skewers. Squeeze over a little lemon, or drizzle with the sherry vinegar to serve.