Preheat oven to 400°F (200°C). Wrap beets individually in aluminum foil and roast for 45 minutes or until tender when pierced with a knife.
Allow beets to cool, then peel skin using a paper towel and cube into 1/2-inch pieces.
In a large mixing bowl, combine the chickpeas, cubed beets, diced red onion, and chopped parsley.
Prepare the vinaigrette by whisking together olive oil, lemon juice, minced garlic, and Dijon mustard in a small bowl until fully emulsified.
Pour the dressing over the chickpea and beet mixture and toss gently to coat.
Carefully fold in the crumbled feta cheese, taking care not to over-mix to prevent the beet juice from staining the cheese entirely.
Season with salt and black pepper to taste and serve immediately or chill for 30 minutes to allow flavors to meld.