Place eggplant in a colander and sprinkle with sea salt; let sit for 30 minutes. Rinse under cold water and pat dry with paper towels.
Preheat the oven to 425 degrees F (220 degrees C). Grease a baking sheet with 1 tablespoon olive oil.
Spread eggplant on the baking sheet in a single layer and drizzle with 2 tablespoons olive oil.
Roast in the preheated oven until golden and crisp, 20 to 25 minutes. Let cool slightly.
Combine roasted eggplant, capers, and garlic in a bowl. Sprinkle with lemon zest. Drizzle lemon juice and remaining 1 tablespoon olive oil on top; toss until evenly coated. Season with salt and pepper. Garnish with fresh parsley.
