Assemble the salad by mixing the coconut, red onion, ginger, tomatoes, chile, lime juice, and salt in a bowl. If using desiccated coconut, hydrate it with a little boiling water first.

Quarter the cabbages lengthwise and brush the cut sides with oil. Place them on a very hot griddle or frying pan until they sizzle and char.

Grill the wedges for 10 to 12 minutes, turning occasionally until they are charred on the edges and tender throughout. Gently toss the coconut mixture into the pan for a few seconds to warm it through before serving.