Place the drained chickpeas in a large mixing bowl. Using a fork or potato masher, mash the chickpeas until mostly broken down but still with some chunky texture remaining.
Add the finely chopped red bell pepper and celery to the mashed chickpeas. Stir until evenly combined, ensuring the vegetables are well distributed.
Pour in the mayonnaise and lemon juice, then sprinkle with ground cumin. Mix thoroughly using a spatula or spoon, until the mixture is cohesive and creamy, with no streaks of mayo.
Season with salt and black pepper to taste. Adjust seasonings as desired, then give the mixture a final stir.
Toast the bread slices lightly if preferred. Spoon the chickpea salad onto one slice of bread, then top with another slice to form a sandwich, or serve as a spread.