Slice the cucumber with the skin lengthwise into narrow slices. Remove the skin from the melon and also slice the flesh into long, narrow slices. Arrange alternately with the cucumber slices on two plates.
Preheat the broiler in the oven to 220 °C. Remove the tomatoes from the oil and finely dice them, chop the nuts. Pluck basil leaves from stems and chop finely.
Finely grate half of the orange peel, squeeze out the juice. Slit vanilla bean lengthwise and scrape out pith. Whisk vanilla pulp with orange zest, juice, pepper, salt, sugar and oil to a smooth marinade. Fold in the diced tomatoes, nuts and basil.
Grill the goat cheese in the heated oven grill for 1 to 2 minutes, place on the plates in the center of the carpaccio and bring the whole to the table drizzled with the marinade.
Tips: The slices for the carpaccio are best shaved with a peeler. Never grate the orange peel too deeply, because if you catch the white part of the peel, the grated orange will have a bitter taste.
To prevent the orange peel from sticking to the grater, simply place a sheet of sandwich paper or parchment paper over the teeth to remove the grating easily.