Make lines or indentations lengthwise down cucumber at 1/4-inch intervals, using vegetable peeler or tines of fork. Cut cucumber into 32 slices, 1/2 inch each. Place on paper towels to drain.
Spread each slice with about 1 teaspoon tomato spread. Sprinkle each with about 1/2 teaspoon cheese.
Serve immediately, or refrigerate up to 1 hour. Top each slice with basil leaf just before serving.