Peel cucumber, slice in half, slice into 1/4-inch thick half moons. Scatter on the bottom of the bowl.
Slice tomatoes into 8 wedges, removing core. Place on top cucumbers.
Scatter feta cheese over cucumbers and tomatoes.
Finely shred half of the basil leaves, sprinkle on salad. Place remaining leaves on salad whole, or if very large, torn into pieces.
Sprinkle with a small amount of dried oregano.
Drizzle with olive oil.
Serve immediately.