Cook eggs: Fill a small saucepan with water and bring to a boil. Carefully add 2 large eggs to boiling water and cook for 10 minutes over medium heat. Immediately drain and return to saucepan. Cover and shake pan to gently crack shells, then fill saucepan with ice water. Let stand until step 5.

Prep ingredients: Rinse and drain chickpeas. Finely chop 1 teaspoon garlic, then lightly crush the 2nd garlic clove. Coarsely chop roasted red peppers.

Season chickpeas: Heat 1 tablespoon oil in a medium skillet over medium. Add chopped garlic; cook, stirring, until fragrant, about 1 minute. Add chickpeas and roasted red peppers. Increase heat to medium-high and cook, stirring, until chickpeas are warm, about 3 minutes. Off the heat, stir in 2 teaspoons vinegar and 1 teaspoon oil. Season with salt and pepper.

Make vinaigrette: Preheat broiler with top rack 6 inches from heat source. Pick and finely chop dill fronds, discarding stems. In a medium bowl, whisk together 1 tablespoon vinegar, 1 teaspoon water, and 3 tablespoons oil. Season to taste with salt and pepper. Stir in half of the chopped dill. Reserve 2 tablespoons of the vinaigrette in a small bowl.

Prep salad: Crumble feta. Chop olives, removing any pits. Cut tomatoes into ½-inch pieces. Halve romaine lengthwise, then cut crosswise into ½-inch pieces. Thinly slice cucumber (peel if desired). Peel eggs under running water; cut into quarters. Drizzle pitas all over with oil; broil directly on top rack until toasted, 1–2 minutes per side (watch closely).

Finish & serve: Rub pitas with crushed garlic clove, then cut into wedges. Season with salt. Add romaine and half each of feta and dill to bowl with vinaigrette; toss and season with salt and pepper. Top with chickpeas, eggs, cucumbers, tomatoes, and olives. Drizzle with reserved vinaigrette. Garnish with remaining dill and feta.