Ask your fishmonger to clean the scallops for you to take the roe out. You should end up with just the white meaty part. Chill the scallops in the fridge so it is easier to slice them in half, along the centre horizontally. Cut the carrot about 5cm long and about the same thickness as a matchstick) and blanch them in salted boiling water until al dente. Slice the cucumber the same way as the carrots, using only thegreen part (no seeds). There is no need to cook the cucumber, only slice it.
For the sauce, place the water and the juice of half a lemon in a pan, reduce by half and, with a whisk, add the butter a little at a time and season with salt.
For the flavoured breadcrumbs just mix the breadcrumbs with olive oil, salt, black pepper and chopped parsley to taste.
To serve, mix the carrots and cucumber, then season with salt and extra virgin olive oil, and place in the centre of the plate. Cook the scallops in a hot pan with some vegetable oil for about 2 minutes on either side. Dust the scallops with the flavoured breadcrumbs and place the scallop on top of the vegetables. Reheat the sauce if required and spoon around the scallops.