Gather all ingredients.
Place potatoes in a large saucepan. Fill with enough water to cover potatoes. Bring to a boil, then reduce heat to medium-low. Cook potatoes until tender but not mushy, 10 to 15 minutes. Drain potatoes in a colander. Transfer to a bowl. Let cool and dry out a little, about 10 minutes.
Preheat the oven to 450 degrees F (230 degrees C). Line a 10x15-inch baking sheet with foil. Drizzle cooled potatoes with 2 tablespoons olive oil and sprinkle with salt and pepper; toss to coat.
Place potatoes in a single layer on the prepared baking sheet. Use a potato masher or the heel of your hand to lightly press down on potatoes to crush them.
Bake potatoes until just beginning to crisp on the bottoms, 20 minutes.
Meanwhile, whisk remaining 2 tablespoons olive oil, lemon juice, garlic, and Greek seasoning in a small bowl until well combined. Spoon the oil mixture over each smashed potato.
Return potatoes to the oven and continue baking until bottoms are crispy, about 10 minutes more.
Transfer crispy potatoes to a shallow serving bowl and add the feta cheese, green onion, and parsley; gently toss to combine. Serve warm with lemon wedges.
