To prepare the whipped feta, combine the cream cheese, feta cheese, and olive oil in a food processor. Process on high until the mixture is completely whipped, smooth, and creamy, which should take about two to three minutes.
Next, in a medium-sized bowl, mix the cherry tomatoes, red onion, green pepper, kalamata olives, and cucumbers. Add the oregano, lemon juice, and olive oil, then season with salt and pepper to taste.
To assemble the dish, spoon the whipped feta onto slices of sourdough bread. Top with the Greek salad mixture and garnish with fresh oregano. For an extra touch, drizzle with additional extra virgin olive oil if desired. Enjoy immediately!