Rinse the quinoa under cold water. In a medium saucepan, combine the rinsed quinoa with 2 cups of water. Bring to a boil over medium heat, then reduce heat to low, cover, and let simmer for 15 minutes. Remove from heat and let cool.
If using canned chickpeas, drain and rinse them. If using dried chickpeas, soak overnight and boil until tender (1 to 2 hours). Let cool before adding to the salad.
Chop the cherry tomatoes, cucumber, bell pepper, red onion, and parsley.
In a small bowl, whisk together olive oil, lemon juice, Dijon mustard, salt, and pepper.
In a large bowl, combine chickpeas, cherry tomatoes, cucumber, bell pepper, red onion, parsley, and cooled quinoa. Pour the lemon vinaigrette over and toss gently to combine.
Taste and adjust seasoning if needed. Serve immediately or refrigerate for 30 minutes to meld flavors.