This appetizer packs a big flavor punch for such a light dish. It's ideal for a cocktail party or dinner buffet. For a slightly different taste and crisper texture, substitute large celery stalks for the cucumber. The pesto is made with walnuts instead of pine nuts for a slight twist; any leftovers can be stored in an airtight container in the refrigerator for up to a week.
Cut each cucumber in half lengthwise and again in half crosswise to make 4 stocky pieces.
Use a spoon to remove the seeds and hollow out a shallow trough in each piece.
Lightly salt each piece and set aside on a platter.
In a blender or food processor, combine the basil, garlic, walnuts, Parmesan cheese, and olive oil and blend until smooth.
Use a spoon to spread pesto into each cucumber "boat" and sprinkle each with paprika.
Serve.