Parboil the potatoes. Preheat an oven to 425°F/220°C. Place potatoes in a medium pot, then cover with cool water. Set over high heat, bring to a boil, then cook until tender, about 8-10 minutes. Drain, cool for 5-10 minutes, then transfer to a parchment lined baking sheet, leaving a few inches.
Smash the potatoes. Place a piece of parchment paper on top of the potatoes, then use a large cup to press down firmly, smashing each potato individually so they are about ¼-½-inch thick. It’s ok if small pieces break off, but in general you want them to remain intact. Remove the top piece of parchment paper, discard, then drizzle potatoes with 2 Tbsp olive oil, 1 tsp Kosher salt, and ¼ tsp black pepper.
Roast the potatoes. Transfer to the preheated oven and roast for 20-30 minutes (this depends on the size and thickness of the potatoes), or until the edges are crispy, but the centers remain tender and fluffy.
Make the caper sauce. In a small bowl, whisk together ¼ cup extra virgin olive oil, 3 Tbsp fresh lemon juice, 2 tsp lemon zest, 1 finely chopped shallot, 2 Tbsp chopped capers, and 2 Tbsp chopped dill. Stir well.
Serve warm! Drizzle the caper sauce over the potatoes, then garnish with feta cheese and freshly cracked black pepper. Serve immediately!