Preheat the oven to 400°F. Pat the chickpeas dry with a clean towel, then toss them with olive oil, salt, and pepper. Spread them out on a baking sheet and roast for 20-25 minutes, shaking the pan halfway, until golden and crispy.
Bring a large pot of salted water to a boil. Cook the pasta according to the package instructions. Drain, then toss a few ice cubes into the colander with the hot pasta. Stir gently until the ice melts, cooling the pasta quickly. Set aside to cool completely.
If the Caesar dressing feels too thick, stir in a splash of lemon juice or white vinegar to thin it out.
In a large mixing bowl, toss the cooled pasta with the Caesar dressing until evenly coated. Add the roasted chickpeas and arugula, folding gently to combine.
Sprinkle crumbled croutons on top for added crunch. Finish with shaved Parmesan and any optional toppings, like cherry tomatoes or grilled chicken. Serve chilled or at room temperature.
