In a medium saucepan, heat the 4 tablespoons of oil. Add the onion, olives and oregano and cook over moderately low heat. Stir until the onion is softened, about 7 minutes. Remove from heat and add both vinegars. Season with salt. Cool to room temperature.

Toss the cucumbers in a small bowl, with 1/2 tablespoon of honey and season with a pinch of salt. In a blender, puree the chopped tomatoes with the remaining 1/2 tablespoon of honey and season generously with salt and pepper.

Pour the pureed soup into shallow bowls. Top with the onion-olive mixture, cherry tomatoes, cucumber slices and feta. Drizzle with olive oil, garnish with greens or oregano leaves and serve.