Bring a small pot of water to a rolling boil. Gently place the eggs into the boiling water using a large spoon or strainer. Set a timer for 6 minutes. With a minute left, prepare a large bowl of ice water. When the timer goes off, transfer the eggs to the ice water. Let completely cool.
Combine the shaved cucumber and radish in a small bowl. Add the lemon juice, white wine vinegar, and 1 tablespoon of olive oil. Mix well and season with salt to taste. Set aside.
Heat a large 12” skillet over medium heat. Add enough olive oil to generously coat the bottom. Once the oil is hot, add the bread cubes. Let cook until golden and toasted, stirring often to crisp all sides. Transfer the croutons to paper towels and season with a pinch of salt.
Combine the feta cheese, greek yogurt, water, and 3 tablespoons of olive oil in a food processor. Process until smooth and creamy. Do not add any salt (the feta is salty enough).
To plate, spread the whipped feta onto the bottom of a large plate. Peel the jammy eggs and slice each one in half. Arrange them on top of the feta with a pinch of salt on each. Arrange the croutons, cucumbers, and radish to fill in the holes. Garnish with fresh dill, minced chives, and freshly cracked black pepper.