Preheat oven to 425°F. Grease a large baking sheet with olive oil and set aside.

Bring a large pot of salted water to a boil. Add the potatoes and cook until fork tender, about 15 to 20 minutes. Drain and let cool for 5 minutes.

Place potatoes on the greased baking sheet. Gently press down on the potatoes until smashed but still in one piece, about 1/2-inch thick.

Drizzle potatoes with olive oil and season generously with salt and pepper. Bake until crispy, about 25 to 30 minutes. Remove from the oven and let cool for 10 minutes.

In a large bowl, whisk together Greek yogurt, mayonnaise, dill, parsley, shallot, garlic, Dijon, lemon juice, red wine vinegar, salt, and pepper.

When potatoes are cool, add them to the bowl with the dressing. Stir in cucumber, celery, green onions, and dill pickles. Taste and adjust seasoning with salt and pepper if necessary. Garnish with feta cheese and serve.