Place a baking sheet on the lowest oven rack; preheat to 425 degrees F. Heat 1 tablespoon olive oil in a large skillet over high heat. Add the chickpeas, spinach, scallion whites, coriander, 1/4 teaspoon salt and a few grinds of pepper. Cook, tossing, until the spinach wilts, about 2 minutes. Transfer the mixture to a colander to drain; let cool slightly. Wipe out the skillet and reserve.
Whisk the eggs, half-and-half, lemon zest, 1/2 teaspoon salt and a few grinds of pepper in a large bowl. Spread the spinach mixture in the pie crust and top with the cheese; pour in the egg mixture. Bake on the hot baking sheet until the eggs are set and lightly browned on top, about 30 minutes.
Meanwhile, heat the remaining 1 tablespoon olive oil in the reserved skillet over medium-high heat. Add the bell peppers and season with 1/4 teaspoon salt and a few grinds of pepper. Cook, stirring, until golden, about 3 minutes. Add 2 tablespoons water; cover and cook until the bell peppers soften, about 2 minutes. Stir in the scallion greens, then remove from the heat. Add the lemon juice and toss. Cut the quiche into wedges; serve with the bell peppers.