How to Make It
Preheat oven to 350°F. Toss together bread sticks and 1 tablespoon olive oil on a large rimmed baking sheet, and season to taste with salt and pepper. Bake in preheated oven until golden and just crisp, about 10 minutes. Let cool.
Meanwhile, bring a medium saucepan of water to a boil. Using a slotted spoon, carefully lower eggs into boiling water, and cook for exactly 7 minutes. Plunge eggs into a bowl of ice water; let stand until cool. Drain well. Carefully peel and halve eggs.
Whisk together lemon juice, honey, and remaining 1/4 cup olive oil in a large bowl, and season to taste with salt and pepper. Add escarole, radicchio, and parsley, and toss well to coat. Season to taste with salt and pepper, and toss again. Transfer to 4 plates or a platter, and arrange eggs and bread sticks on top. Generously dust the salad with pimentón, and serve immediately.