Wash the prawns well in lots of cold water. Drain them and cut them in half lengthwise with their shells on, but leave the tails intact to hold the two halves together. It is easy to cut them if you start from the belly. You can leave the legs on (I do) or take them off before you make the cut. Remove the alimentary canal. The blue "vein" is just that, and not harmful. Rub some of the olive oil all over the prawns; it doesn't take much. Put the prawns in the refrigerator to marinate in the oil for about 2 hours or more, if possible.

Prepare the fire in the wood grill and when the coals are medium hot, gently oil the grate over the fire with some olive oil. If you are using the broiler, preheat it for at least 12 minutes. Place the prawns on the grate over the coals cut side down and cook them for 1 minute. Turn them over with a spatula or tongs, sprinkle with some salt and pepper, and let them cook not more than another minute or they will dry out. If you have a good strong fire this should be enough time. If you think it is not, leave them on another minute or so more, but do not overcook them or they will be tough. If you are using a broiler, put the prawns on a lightly oiled grate or pan and get them as close to the heat as you can, almost touching.

Core the tomatoes and slice them as thin as you can, about 1/8 inch, and cover the bottom of six warm plates with the slices. Drizzle on a thin thread of olive oil and scatter on some chopped basil. Sprinkle on a little salt and pepper. Keep the plates as warm as you can. As the prawns are done, arrange three of them on each tomato-lined plate, cut side up. Serve immediately. Spoon some salmoriglio sauce all over them, being generous, and serve more at the table. Homemade crunchy bread is ideal to serve with the prawns.