Whisk chopped nuts, pepper, vinegar and honey in a small bowl. Gradually stream in oil, whisking constantly until emulsified; generously season dressing with salt and pepper.
Using a mandoline, shave cucumber and cantaloupe lengthwise (or thinly slice with a knife). Place in a large bowl; add basil and nuts. Drizzle dressing over and toss gently to coat. Season once again with salt and pepper, to taste; and serve.